
%%%%%%%%%%%%%%%%%%[basicstyle=\footnotesize\ttfamily]%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Package pgfplots.sty documentation.
%
% Copyright 2007-2009 by Christian Feuersaenger.
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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\ifdefined\pdfvariable
    \pdfvariable minorversion=5
    \pdfvariable objcompresslevel=2
\else\ifdefined\XeTeXversion
    \special{pdf:minorversion 5}
    \special{dvipdfmx:config z 2} % also sets normal compresslevel=2
\else
    \pdfminorversion=5 % to allow compression
    \pdfobjcompresslevel=2
\fi\fi
\documentclass[a4paper]{ltxdoc}
\input{pgfplots.preamble.tex}

\usepackage{array}
\usepackage{colortbl}
\usepackage{booktabs}
\usepackage{eurosym}
\usepackage{multirow}

\pgfqkeys{/codeexample}{%
    every codeexample/.style={
        width=4cm,
        /pgfplots/every axis/.append style={legend style={fill=graphicbackground}}
    },
    narrow/.style={width=7cm},
    tabsize=4,
}

\pgfkeys{/pgfmanual/gray key prefixes/.add={/pgfplots/table/,/pgf/number format/,}{}}

\makeatletter
\pgfkeys{%
    /codeexample/prettyprint/key name with handler/.code 2 args={%
        \gdef\pgfplotstablemanualautocheck{}%
        \foreach \special in {columns,create on use,alias,display columns}{%
            \expandafter\pgfutil@in@\expandafter{\special/}{#1}%
            \ifpgfutil@in@
                \xdef\pgfplotstablemanualautocheck{\special}%
                \breakforeach
            \fi
        }%
        \ifx\pgfplotstablemanualautocheck\pgfutil@empty%
            \pgfmanualpdfref{#1}{#1}/\pgfmanualpdfref{/handlers/#2}{#2}%
        \else
            \expandafter\def\expandafter\temp\expandafter##\expandafter1\pgfplotstablemanualautocheck/##2\relax{%
                \pgfmanualpdfref
                    {/pgfplots/table/\pgfplotstablemanualautocheck}%
                    {##1\pgfplotstablemanualautocheck/}%
                ##2/%
                \pgfmanualpdfref{/handlers/#2}{#2}%
            }%
            \temp#1\relax
        \fi
    },
    /pdflinks/search key prefixes in/.add={/pgf/number format/,}{,/pgfplots/table/create col/},
    /pdflinks/show labels=false,
}
\makeatother

\pgfplotstableset{
    %debug=true,
    begin table=\begin{tabular}[b],
}

\title{%
    Manual for Package \PGFPlotstable{}\\
    {\small Component of \PGFPlots{}, Version \pgfplotsversion}\\
    {\small\href{http://sourceforge.net/projects/pgfplots}{http://sourceforge.net/projects/pgfplots}}}

\begin{document}
\maketitle
\begin{abstract}
    This package reads tab-separated numerical tables from input and generates
    code for pretty-printed \LaTeX{}-tabulars. It rounds to the desired precision
    and prints it in different number formatting styles.
\end{abstract}

\tableofcontents


\section{Introduction}

\PGFPlotstable{} is a lightweight sub-package of \PGFPlots{} which employs its
table input methods and the number formatting techniques to convert
tab-separated tables into tabulars.

Its input is a text file containing space-separated rows, possibly starting
with column names. Its output is a \LaTeX{} tabular\footnote{Please see the
remarks in Section~\ref{sec:pgfplotstable:context} for plain \TeX{} and
Con\TeX{}t.} which contains selected columns of the text table, rounded to the
desired precision, printed in the desired number format (fixed point, integer,
scientific etc.). The output is \LaTeX{} code, and that code is finally typeset
by \LaTeX{}.

In other words, \PGFPlotstable{} is nothing but a more-or-less smart code
generator which spits out something like |\begin{tabular}...\end{tabular}|.
Use it if you'd like to customize row or column dependent styles or if you
have numerical data for which you want to have automatically formatted content.

It is used with
%
% NO GALLERY
\begin{codeexample}[code only]
\usepackage{pgfplotstable}
% recommended:
%\usepackage{booktabs}
%\usepackage{array}
%\usepackage{colortbl}
\end{codeexample}
%
\noindent and requires \PGFPlots{} and \PGF{} $ \ge 2.00$ installed.

\begin{command}{\pgfplotstableset\marg{key-value-options}}
    The user interface of this package is based on key-value-options. They
    determine what to display, how to format and what to compute.

    Key--value pairs can be set in two ways:
    %
    \begin{enumerate}
        \item As default settings for the complete document (or maybe a part
            of the document), using |\pgfplotstableset|\marg{options}. For
            example, the document's preamble may contain
            %
% NO GALLERY
\begin{codeexample}[code only]
\pgfplotstableset{fixed zerofill,precision=3}
\end{codeexample}
            %
            to configure a precision of $3$ digits after the period, including
            zeros to get exactly $3$ digits for all fixed point numbers.
        \item As option which affects just a single table. This is provided
            as optional argument to the respective table typesetting command,
            for example |\pgfplotstabletypeset|\oarg{options}\marg{file}.
    \end{enumerate}
    %
    Both ways are shown in the examples below.

    Knowledge of |pgfkeys| is useful for a deeper insight into this package, as
    |/.style|, |/.append style| etc.\@ are specific to |pgfkeys|. Please refer
    to the \PGF{} manual~\cite[Section ``pgfkeys'']{tikz} or the shorter
    introduction~\cite{keyvalintro} to learn more about |pgfkeys|. Otherwise,
    simply skip over to the examples provided in this document.

    You will find key prefixes |/pgfplots/table/| and |/pgf/number format/|.
    These prefixes can be skipped if they are used in \PGFPlotstable{}; they
    belong to the ``default key path'' of |pgfkeys|.
\end{command}


\section{Loading and Displaying data}

\subsection{Text Table Input Format}

\PGFPlotstable{} works with plain text file tables in which entries (``cells'')
are separated by a separation character. The initial separation character is
``white space'' which means ``at least one space or tab'' (see option |col sep|
below). Those tables can have a header line which contains column names and
most other columns typically contain numerical data.

\noindent The following listing shows |pgfplotstable.example1.dat| and is used
often throughout this documentation.
%
\begin{codeexample}[code only]
# Convergence results
# fictional source, generated 2008
level    dof      error1            error2   info     grad(log(dof),log(error2)) quot(error1)
1        4        2.50000000e-01    7.57858283e-01    48       0                 0
2        16       6.25000000e-02    5.00000000e-01    25       -3.00000000e-01   4
3        64       1.56250000e-02    2.87174589e-01    41       -3.99999999e-01   4
4        256      3.90625000e-03    1.43587294e-01    8        -5.00000003e-01   4
5        1024     9.76562500e-04    4.41941738e-02    22       -8.49999999e-01   4
6        4096     2.44140625e-04    1.69802322e-02    46       -6.90000001e-01   4
7        16384    6.10351562e-05    8.20091159e-03    40       -5.24999999e-01   4
8        65536    1.52587891e-05    3.90625000e-03    48       -5.35000000e-01   3.99999999e+00
9        262144   3.81469727e-06    1.95312500e-03    33       -5.00000000e-01   4.00000001e+00
10       1048576  9.53674316e-07    9.76562500e-04    2        -5.00000000e-01   4.00000001e+00
\end{codeexample}
%
Lines starting with `|%|' or `|#|' are considered to be comment lines and are
ignored.

\begin{command}{\pgfplotstabletypeset\oarg{optional arguments}\marg{file name {\normalfont or} \textbackslash macro {\normalfont or} inline table}}
    Loads (or acquires) a table and typesets it using the current configuration
    of number formats and table options.

    In case the first argument is a file name, the table will be loaded from
    disk. If it is an already loaded table (see |\pgfplotstableread| or
    |\pgfplotstablenew|), it will be used. Otherwise, if it is inline table
    data, this data will be parsed just as if it was found in a file (see
    |\pgfplotstableread|).
    %
\begin{codeexample}[]
\pgfplotstabletypeset[sci zerofill]{
    a b
    5000 1.234e5
    6000 1.631e5
    7000 2.1013e5
    9000 1000000
}
\end{codeexample}

\begin{codeexample}[]
\pgfplotstabletypeset{pgfplotstable.example1.dat}
\end{codeexample}

    \noindent The configuration can be customized with \meta{optional
    arguments}. Configuration can be done for the complete table or for
    particular columns (or rows).

\begin{codeexample}[]
\pgfplotstableset{% global config, for example in the preamble
    % these columns/<colname>/.style={<options>} things define a style
    % which applies to <colname> only.
    columns/dof/.style={int detect,column type=r,column name=\textsc{Dof}},
    columns/error1/.style={
        sci,sci zerofill,sci sep align,precision=1,sci superscript,
        column name=$e_1$,
    },
    columns/error2/.style={
        sci,sci zerofill,sci sep align,precision=2,sci 10e,
        column name=$e_2$,
    },
    columns/{grad(log(dof),log(error2))}/.style={
        string replace={0}{}, % erase '0'
        column name={$\nabla e_2$},
        dec sep align,
    },
    columns/{quot(error1)}/.style={
        string replace={0}{}, % erase '0'
        column name={$\frac{e_1^{(n)}}{e_1^{(n-1)}}$}
    },
    empty cells with={--}, % replace empty cells with '--'
    every head row/.style={before row=\toprule,after row=\midrule},
    every last row/.style={after row=\bottomrule}
}
\pgfplotstabletypeset[ % local config, applies only for this table
    1000 sep={\,},
    columns/info/.style={
        fixed,fixed zerofill,precision=1,showpos,
        column type=r,
    }
]
{pgfplotstable.example1.dat}
\end{codeexample}

    \noindent All of these options are explained in all detail in the following
    sections.

    You may also use an input format similar to the tabular environment:
    %
\begin{codeexample}[width=8cm]
\pgfplotstabletypeset
    [col sep=&,row sep=\\,sci zerofill]
{
    level &  dof &    error \\
    1 &      4 &      2.50000000e-01 \\
    2 &      16 &     6.25000000e-02 \\
    3 &      64 &     1.56250000e-02 \\
    4 &      256 &    3.90625000e-03 \\
    5 &      1024 &   9.76562500e-04 \\
    6 &      4096 &   2.44140625e-04 \\
    7 &      16384 &  6.10351562e-05 \\
    8 &      65536 &  1.52587891e-05 \\
    9 &      262144 & 3.81469727e-06 \\
    10 &     1048576 &9.53674316e-07 \\
}
\end{codeexample}

    Technical note: every opened file will be protocolled into your logfile.
\end{command}

\begin{command}{\pgfplotstabletypesetfile\oarg{optional arguments}\marg{file name}}
    Loads the table \meta{file name} and typesets it. As of \PGFPlotstable{}
    1.2, this command is an alias to |\pgfplotstabletypeset|, that means the
    first argument can be either a file name or an already loaded table.
\end{command}

\begin{commandlist}{%
    \pgfplotstableread\marg{file name}\marg{\textbackslash macro},
    \pgfplotstableread\marg{inline table}\marg{\textbackslash macro}%
}
    Loads a table into the \TeX{} macro \meta{\textbackslash macro}. This macro
    will store the table as internal structure and can be used multiple times.
    %
\begin{codeexample}[]
\pgfplotstableread{pgfplotstable.example1.dat}\loadedtable
\pgfplotstabletypeset[columns={dof,error1}]\loadedtable
\hspace{2cm}
\pgfplotstabletypeset[columns={dof,error2}]\loadedtable
\end{codeexample}
    %
    The first argument can be a \meta{file name} as in the example here. It is
    also possible to provide the table data directly:
    %
\begin{codeexample}[code only]
% Alternative: inline table data:
\pgfplotstableread{
level   dof     error1  error2  info    grad(log(dof),log(error2))      quot(error1)
1       4       2.50000000e-01  7.57858283e-01  48      0               0
2       16      6.25000000e-02  5.00000000e-01  25      -3.00000000e-01 4
3       64      1.56250000e-02  2.87174589e-01  41      -3.99999999e-01 4
4       256     3.90625000e-03  1.43587294e-01  8       -5.00000003e-01 4
5       1024    9.76562500e-04  4.41941738e-02  22      -8.49999999e-01 4
6       4096    2.44140625e-04  1.69802322e-02  46      -6.90000001e-01 4
7       16384   6.10351562e-05  8.20091159e-03  40      -5.24999999e-01 4
8       65536   1.52587891e-05  3.90625000e-03  48      -5.35000000e-01 3.99999999e+00
9       262144  3.81469727e-06  1.95312500e-03  33      -5.00000000e-01 4.00000001e+00
10      1048576 9.53674316e-07  9.76562500e-04  2       -5.00000000e-01 4.00000001e+00
}\loadedtable
% can be used as above:
\pgfplotstabletypeset[columns={dof,error1}]\loadedtable
\hspace{2cm}
\pgfplotstabletypeset[columns={dof,error2}]\loadedtable
\end{codeexample}
    %
    It is checked automatically whether the first argument contains inline data
    or a file name.

    This check whether the first argument is inline data or a file name works
    as follows: if |format=auto|, the first argument is considered to be a file
    name unless it contains the |row sep| character (see |row sep|). If
    |format=inline|, it is always considered to be inline data. If
    |format=file|, it is a file name.


    \paragraph{Special cases and more details:}

    \begin{itemize}
        \item The inline data format is ``fragile''. If you experience
            problems, terminate your tables with `|\\|' combined with
            |row sep=\\| (the docs for |row sep| contain alternative ways and
            more explanation).
        \item There are variants of this command which do not really build up
            a struct, but which report every line to a ``listener''. There is
            also a struct which avoids protection by \TeX{} scopes. In case
            you need such things, consider reading the source code comments.
        \item Technical note: every opened file will be protocolled into your
            logfile.
        \item Note: avoid using `|\table|' as name, it conflicts with
            |\begin{table}| of \LaTeX{}.
    \end{itemize}
\end{commandlist}

\begin{key}{/pgfplots/table/col sep=\mchoice{space,tab,comma,semicolon,colon,braces,\&,ampersand} (initially space)}
    Specifies the column separation character for table reading. The initial
    choice, |space|, means ``at least one white space''. White spaces are tab
    stops or spaces (newlines characters always delimit lines).

    For example, the file |pgfplotstable.example1.csv| uses commas as
    separation characters.
    %
\begin{codeexample}[code only]
# Convergence results
# fictional source generated 2008
level,dof,error1,error2,info,{grad(log(dof),log(error2))},quot(error1)
1,9,2.50000000e-01,7.57858283e-01,48,0,0
2,25,6.25000000e-02,5.00000000e-01,25,-1.35691545e+00,4
3,81,1.56250000e-02,2.87174589e-01,41,-1.17924958e+00,4
4,289,3.90625000e-03,1.43587294e-01,8,-1.08987331e+00,4
5,1089,9.76562500e-04,4.41941738e-02,22,-1.04500712e+00,4
6,4225,2.44140625e-04,1.69802322e-02,46,-1.02252239e+00,4
7,16641,6.10351562e-05,8.20091159e-03,40,-1.01126607e+00,4
8,66049,1.52587891e-05,3.90625000e-03,48,-1.00563427e+00,3.99999999e+00
9,263169,3.81469727e-06,1.95312500e-03,33,-1.00281745e+00,4.00000001e+00
10,1050625,9.53674316e-07,9.76562500e-04,2,-1.00140880e+00,4.00000001e+00
\end{codeexample}
    %
    Thus, we need to specify |col sep=comma| when we read it.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[col sep=comma]{pgfplotstable.example1.csv}
\end{codeexample}
    %
    You may call |\pgfplotstableset{col sep=comma}| once in your preamble if
    all your tables use commas as column separator.

    Please note that if cell entries (for example column names) contain the
    separation character, you need to enclose the column entry in
    \emph{braces}: |{grad(log(dof),log(error2)}|. If you want to use unmatched
    braces, you need to write a backslash before the brace. For example the
    name `|column{withbrace|' needs to be written as `|column\{withbrace|'.

    For |col sep|$\neq$|space|, spaces will be considered to be part of the
    argument (there is no trimming). However, (as usual in \TeX{}), multiple
    successive spaces and tabs are replace by a single white space. Of course,
    if |col sep=tab|, tabs are the column separators and will be treated
    specially.

    Furthermore, if you need empty cells in case |col sep=space|, you have to
    provide |{}| to delimit such a cell since |col sep=space| uses \emph{at
    least} one white space (consuming all following ones).

    The value |col sep=braces| is special since it actually uses two separation
    characters. Every single cell entry is delimited by an opening and a
    closing brace, \meta{entry}, for this choice. Furthermore, any white space
    (spaces and tabs) between cell entries are \emph{skipped} in case |braces|
    until the next \meta{entry} is found.

    A further specialty of |col sep=braces| is that it has support for
    \emph{multi-line} cells: everything within balanced braces is considered to
    be part of a cell. This includes newlines:\footnote{This treatment of
    newlines within balanced braces actually applies to every other column
    separator as well (it is a \TeX{} readline feature). In other words: you
    \emph{can} have multi-line cells for every column separator if you enclose
    them in balanced curly braces. However, \texttt{col sep=braces} has the
    special treatment that end-of-line counts as white space character; for
    every other \texttt{col sep} value, this white space is suppressed to
    remove spurious spaces.}

    The |col sep=&| case (probably together with |row sep=\\|) allows to read
    tables as you'd usually type them in \LaTeX{}. This will automatically enable
    |trim cells|.
\end{key}

\begin{key}{/pgfplots/table/trim cells=\mchoice{true,false} (initially false)}
    If enabled, leading and trailing white space will be removed while tables
    are read.

    This might be necessary if you have |col sep|$\neq$|space| but your cells
    contain spaces. It will be activated automatically for |col sep=&|.
\end{key}

\begin{key}{/pgfplots/table/header=\mchoice{true,false,has colnames} (initially true)}
    Configures if column names shall be identified automatically during input
    operations.

    The first non-comment line \emph{can} be a header which contains column
    names. The |header| key configures how to detect if that is really the
    case.

    The choice \declaretext{true} enables auto detection of column names: If
    the first non-comment line contains at least one non-numerical entry (for
    example `|a name|'), each entry in this line is supposed to be a column
    name. If the first non-comment line contains only numerical data, it is
    used as data row. In this case, column indices will be assigned as column
    ``names''.

    The choice \declaretext{false} is identical to this last case, i.e.\@ even
    if the first line contains strings, they won't be recognised as column
    names.

    Finally, the choice \declaretext{has colnames} is the opposite of |false|:
    it assumes that the first non-comment line \emph{contains} column names.
    In other words: even if only numbers are contained in the first line, they
    are considered to be column \emph{names}.

    Note that this key only configures headers in \emph{input} tables. To
    configure \emph{output} headers, you may want to look at |every head row|.
\end{key}

\begin{pgfplotskey}{table/format=\mchoice{auto,inline,file} (initially auto)}
    Configures the format expected as first argument for
    |\pgfplotstableread|\marg{input}.

    The choice \declaretext{inline} expects the table data directly as argument
    where rows are separated by |row sep|. Inline data is ``fragile'', because
    \TeX{} may consume end-of-line characters (or |col sep| characters). See
    |row sep| for details.

    The choice \declaretext{file} expects a file name.

    The choice \declaretext{auto} searches for a |row sep| in the first
    argument supplied to |\pgfplotstableread|. If a |row sep| has been found,
    it is inline data, otherwise it is a file name.
\end{pgfplotskey}

\begin{pgfplotskey}{table/row sep=\mchoice{newline,\string\\} (initially newline)}
    Configures the character to separate rows of the inline table data format
    (see |format=inline|).

    The choice \declaretext{newline} uses the end of line as it appears in the
    table data (i.e.\@ the input file or any inline table data).

    The choice \declaretext{\string\\} uses `|\\|' to indicate the end of a
    row.

    Note that \declaretext{newline} for inline table data is ``fragile'': you
    can't provide such data inside of \TeX{} macros (this does not apply to
    input files). Whenever you experience problems, proceed as follows:
    %
    \begin{enumerate}
        \item First possibility: call
            |\pgfplotstableread|\marg{data}|\yourmacro| \emph{outside} of any
            macro declaration.
        \item Use |row sep=\\|.
    \end{enumerate}
    %
    The same applies if you experience problems with inline data and special
    |col sep| choices (like |col sep=tab|).

    The reasons for such problems is that \TeX{} scans the macro bodies and
    replaces newlines by white space. It does other substitutions of this sort
    as well, and these substitutions can't be undone (maybe not even found).
\end{pgfplotskey}

\begin{key}{/pgfplots/table/ignore chars=\marg{comma-separated-list} (initially empty)}
    Allows to define an ``ignore list'' for single characters. Any characters
    found in an input file which occur also in \meta{comma-separated-list} will
    silently by thrown away. The processing is exactly the same as if you did
    not write them at all in the first place.

    For example, suppose we are given |pgfplotstable.example5.dat| with
    %
        \lstinputlisting[basicstyle=\ttfamily\footnotesize]{pgfplotstable.example5.dat}

    \noindent then, we can ignore several of the characters by writing
    %
\begin{codeexample}[]
\pgfplotstabletypeset
    [col sep=comma,ignore chars={(,),\ ,\#}]
    {pgfplotstable.example5.dat}
\end{codeexample}

    The \meta{comma-separated-list} should contain exactly one character in
    each list element, and the single characters should be separated by commas.
    Some special characters like commas, white space, hashes, percents or
    backslashes need to be escaped by prefixing them with a backslash.

    Besides normal characters, it is also supported to eliminate any binary
    code from your input files. For example, suppose you have binary characters
    of code |0x01| (hex notation) in your files. Then, use
    %
\begin{codeexample}[code only]
\pgfplotstableset{ignore chars={\^^01}}
\end{codeexample}
    \noindent to eliminate them silently. The |^^|\meta{digit}\meta{digit}
    notation is a \TeX{} feature to provide characters in hexadecimal encoding
    where \meta{digit} is one of |0123456789abcdef|. I don't know if the
    backslash in |\^^01| is always necessary, try it out. There is also a
    character based syntax, in which |\^^M| is \meta{newline} and |\^^I| is
    \meta{tab}. Refer to~\cite{texbook} for more details.

    Note that after stripping all these characters, the input table must be
    valid -- it should still contain column separators and balanced columns.

    This setting applies to |\addplot table| and |\addplot file| for
    \PGFPlots{} as well.

    Note that |ignore chars| is ``fragile'' when it is applied to
    |format=inline| or |format=auto|. Consider |format=file| if you experience
    problems.\footnote{See also |row\ sep| for more information about dealing
    with fragile inline table formats.}
\end{key}

\begin{key}{/pgfplots/table/white space chars=\marg{comma-separated-list} (initially empty)}
    Allows to define a list of single characters which are actually treated
    like white space (in addition to tabs and spaces). It might be useful in
    order to get more than one column separator character.

    The |white space chars| list is used in exactly the same way as
    |ignore chars|, and the same remarks as above apply as well.
\end{key}

\begin{key}{/pgfplots/table/text special chars=\marg{comma-separated-list} (initially empty)}
    Allows to define a list of single characters which are actually treated
    like normal text (like any characters with category code~$12$).

    The |text special chars| list is used in exactly the same way as
    |ignore chars|, and the same remarks as above apply as well.

    Note that some (selected) special characters are installed by
    |verb string type|.
\begin{codeexample}[]
\pgfplotstabletypeset[
    font=\ttfamily,
    verb string type,
]{
URI
http://example.org/a#b
}
\end{codeexample}
\end{key}

\begin{key}{/pgfplots/table/comment chars=\marg{comma-separated-list} (initially empty)}
    Allows to add one or more \emph{additional} comment characters. Each of
    these characters has a similar effect as the |#| character, i.e.\@ all
    following characters of that particular input line are skipped.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[comment chars=!]{
! Some comments
1 0
2 -10
! another comment line
3 0
}
\end{codeexample}
    %
    The example above uses `|!|' as additional comment character (which allows
    to parse Touchstone files).
\end{key}

\begin{key}{/pgfplots/table/percent is letter=\mchoice{true,false} (initially false)}
    Allows to control how to treat percent characters in input files.
    \PGFPlotstable{} used to keep the \TeX{} special meaning as comment
    character which means that all characters following percent where ignored.

    The value \declaretext{true} means that a percent is just a normal letter
    without special meaning. The value \declaretext{false} means that percent
    is special as it used to be.
\end{key}

\begin{key}{/pgfplots/table/text indicator=\marg{char} (initially empty)}
    Allows to define a text indicator character. If this is defined, it can be
    used to enclose delimiters in a cell's body:
    %
\begin{codeexample}[]
\pgfplotstabletypeset[text indicator=",string type]{
A B
"A long cell" normalcell
}
\end{codeexample}

    If the |text indicator| also occurs within the cell, it has to be doubled:
    %
\begin{codeexample}[]
\pgfplotstabletypeset[text indicator=",string type]{
A B
"A long ""cell""" normalcell
}
\end{codeexample}

    Cells which do not start with the text indicator are handled normally. Note
    that |text indicator| does not support multi-line cells.
\end{key}

\begin{key}{/pgfplots/table/skip first n=\marg{integer} (initially 0)}
    Allows to skip the first \meta{integer} lines of an input file. The lines
    will not be processed.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[skip first n=4]{%<- this '%' is important. Otherwise, the
                                      %newline here would delimit an (empty) row.
    XYZ Format,
    Version 1.234
    Date 2010-09-01
    @author Mustermann
    A B C
    1 2 3
    4 5 6
}
\end{codeexample}
\end{key}

% FIXME: duplicate code in pgfplotstable.tex and pgfplots.reference.axis-addplot.tex
\begin{key}{/pgfplots/table/search path=\marg{comma-separated-list} (initially .)}
    Allows to provide a search path for input tables. This variable is
    evaluated whenever \PGFPlots{} attempts to read a data file. This includes
    both |\pgfplotstableread| and |\addplot table|; its value resembles a
    comma-separated list of path names. The requested file will be read from
    the first matching location in that list.

    Use `|.|' to search using the normal \TeX{} file searching procedure
    (i.e.\@ typically in the current working directory).

    An entry in \meta{comma-separated-list} can be relative to the current
    working directory, i.e.\@ something like |search path={.,../datafiles}| is
    accepted.
\end{key}

% FIXME: duplicate code in pgfplotstable.tex and pgfplots.reference.axis-addplot.tex
\begin{key}{/pgfplots/table/search path/implicit .=\mchoice{true,false} (initially true)}
    \PGFPlotstable{} allows to add `|.|' to the value of |search path|
    implicitly as this is typically assumed in many applications of search
    paths.

    The initial configuration |search path/implicit .=true| will ensure that
    `|.|' is added in front of the |search path| if the user value does not
    contain a `|.|'.

    The value |search path/implicit .=false| will not add `|.|'.

    Keep in mind that `|.|' means ``let \TeX{} search for the file on its
    own''. This will typically find files in the current working directory, but
    it will also include processing of |TEXINPUTS|.
\end{key}


\subsection{Selecting Columns and their Appearance Styles}

\begin{key}{/pgfplots/table/columns=\marg{comma-separated-list}}
    Selects particular columns of the table. If this option is empty (has not
    been provided), all available columns will be selected.

    Inside of \meta{comma-separated-list}, column names as they appear in the
    table's header are expected. If there is no header, simply use column
    indices. If there are column names, the special syntax
    |[index]|\meta{integer} can be used to select columns by index. The first
    column has index~$0$.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[columns={dof,level,[index]4}]{pgfplotstable.example1.dat}
\end{codeexample}

    The special |pgfkeys| feature
    |\pgfplotstableset{columns/.add={}{,a further col}}| allows to
    \emph{append} a value, in this case `|,a further col|' to the actual value.
    See |/.add| for details.
\end{key}

\begin{pgfplotstablealiaskey}
    Assigns the new name \meta{col name} for the column denoted by \meta{real
    col name}. Afterwards, accessing \meta{col name} will use the data
    associated with column \meta{real col name}.
    %
\begin{codeexample}[]
% in preamble:
\pgfplotstableset{
    alias/newname/.initial=b,
}

% in document:
\pgfplotstabletypeset[
    columns={a,newname},% access to `newname' is the same as to `b'
]{
    a b
    1 2
    3 4
    5 6
}%
\end{codeexample}
    %
    You can use |columns/|\meta{col name}|/.style| to assign styles for the
    alias, not for the original column name.

    If there exists both an alias and a column of the same name, the column
    name will be preferred. Furthermore, if there exists a |create on use|
    statement with the same name, this one will also be preferred.

    In case \meta{col name} contains characters which are required for key
    settings, you need to use braces around it:
    ``|alias/{name=wi/th,special}/.initial={othername}|''.

    This key is used whenever columns are queried, it applies also to the
    |\addplot table| statement of \PGFPlots{}.
\end{pgfplotstablealiaskey}

\begin{pgfplotstablecolumnkey}
    Sets all options in \meta{key-value-list} exclusively for \meta{column
    name}.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    columns/error1/.style={
        column name=$L_2$,
        sci,sci zerofill,sci subscript,
        precision=3},
    columns/error2/.style={
        column name=$A$,
        sci,sci zerofill,sci subscript,
        precision=2},
    columns/dof/.style={
        int detect,
        column name=\textsc{Dof}
    }
]
    {pgfplotstable.example1.dat}
\end{codeexample}
    %
    If your column name contains commas `|,|', slashes `|/|' or equal signs
    `|=|', you need to enclose the column name in braces.
    %
\begin{codeexample}[narrow]
\pgfplotstabletypeset[
    columns={dof,error1,{grad(log(dof),log(error2))}},
    columns/error1/.style={
        column name=$L_2$,
        sci,sci zerofill,sci subscript,
        precision=3},
    columns/dof/.style={
        int detect,
        column name=\textsc{Dof}},
    columns/{grad(log(dof),log(error2))}/.style={
        column name=slopes $L_2$,
        fixed,fixed zerofill,
        precision=1}
]
    {pgfplotstable.example1.dat}
\end{codeexample}
    %
    If your tables don't have column names, you can simply use integer indices
    instead of \meta{column name} to refer to columns. If you have column
    names, you can't set column styles using indices.
\end{pgfplotstablecolumnkey}

\begin{pgfplotstabledisplaycolumnkey}
    Applies all options in \meta{key-value-list} exclusively to the column
    which will appear at position \meta{index} in the output table.

    In contrast to the |table/columns/|\meta{name} styles, this option refers
    to the output table instead of the input table. Since the output table has
    no unique column name, you can only access columns by index.

    Indexing starts with~$\meta{index}=0$.

    Display column styles override input column styles.
\end{pgfplotstabledisplaycolumnkey}

\begin{stylekey}{/pgfplots/table/every col no \meta{index}}
    A style which is identical with |display columns/|\meta{index}: it applies
    exclusively to the column at position \meta{index} in the output table.

    See |display columns/|\meta{index} for details.
\end{stylekey}

\begin{key}{/pgfplots/table/column type=\marg{tabular column type} (initially c)}
    Contains the column type for |tabular|.

    If all column types are empty, the complete argument is skipped (assuming
    that no |tabular| environment is generated).

    Use |\pgfplotstableset{column type/.add=|\marg{before}\marg{after}|}| to
    \emph{modify} a value instead of overwriting it. The |/.add| key handler
    works for other options as well.
    %
\begin{codeexample}[narrow]
\pgfplotstabletypeset[
    columns={dof,error1,info},
    column type/.add={|}{}% results in '|c'
]
    {pgfplotstable.example1.dat}
\end{codeexample}
\end{key}

\begin{key}{/pgfplots/table/column name=\marg{\TeX{} display column name} (initially \textbackslash pgfkeysnovalue)}
    Sets the column's display name in the current context.

    It is advisable to provide this option inside of a column-specific style,
    i.e.\@ using

    |columns/|\marg{lowlevel colname}|/.style={column name=|\marg{\TeX{} display column name}|}| .

    Here, ``lowlevel colname'' refers to the column name that is present in
    your input table. This lowlevel column name has a couple of restrictions
    (it has to be expandable, for example -- that means many control sequences
    are forbidden). The value of |column name| is only used within
    |\pgfplotstabletypeset| in order to generate a \emph{display} name for the
    column in question.

    Note that you are allowed to provide an \emph{empty} display name using
    |column name={}|. This results in an empty string above the column when
    used in |\pgfplotstabletypeset|.

    The initial configuration is |column name=\pgfkeysnovalue|. This
    constitutes a special ``null'' value which tells |\pgfplotstabletypeset|
    that it should fall back to the column's name (i.e.\@ the lowlevel name).
\end{key}

\begin{codekey}{/pgfplots/table/assign column name}
    Allows to \emph{modify} the value of |column name|.

    Argument |#1| is the current column name, that means after evaluation of
    |column name|. After |assign column| name, a new (possibly modified) value
    for |column name| should be set.

    That means you can use |column name| to assign the name as such and
    |assign column name| to generate final \TeX{} code (for example to insert
    |\multicolumn{1}{c}{#1}|).
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    assign column name/.style={
        /pgfplots/table/column name={\textbf{#1}}
    },
]
{
first second
1 2
3 4
}
\end{codeexample}

    Note that the \PGFPlotstable{} provides limited postprocessing capabilities
    for headers, in particular, |postproc cell content| and its friends merely
    apply to ``normal'' cells. If you want to modify the appearance of header
    cells, you should consider using |assign column name|.

    Default is empty which means no change.
\end{codekey}

\begin{stylekey}{/pgfplots/table/multicolumn names=\marg{tabular column type} (initially c)}
    A style which typesets each column name in the current context using a
    |\multicolumn{1}|\marg{tabular column type}\marg{the column name}
    statement.

    Here,\meta{the column name} is set with |column name| as usual.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/dec sep align=\marg{header column type} (initially c)}
    A style which aligns numerical columns at the decimal separator.

    The first argument determines the alignment of the header column.

    Please note that you need |\usepackage{array}| for this style.
    %
\begin{codeexample}[]
% requires \usepackage{array}
\pgfplotstabletypeset[
    columns={dof,error1,error2,info,{grad(log(dof),log(error2))}},
    columns/error1/.style={dec sep align},
    columns/error2/.style={sci,sci subscript,sci zerofill,dec sep align},
    columns/info/.style={fixed,dec sep align},
    columns/{grad(log(dof),log(error2))}/.style={fixed,dec sep align}
]
    {pgfplotstable.example1.dat}
\end{codeexample}

    Or with comma as decimal separator:
    %
\begin{codeexample}[]
% requires \usepackage{array}
\pgfplotstabletypeset[
    use comma,
    columns={dof,error1,error2,info,{grad(log(dof),log(error2))}},
    columns/error1/.style={dec sep align},
    columns/error2/.style={sci,sci subscript,sci zerofill,dec sep align},
    columns/info/.style={fixed,dec sep align},
    columns/{grad(log(dof),log(error2))}/.style={fixed,dec sep align}
]
    {pgfplotstable.example1.dat}
\end{codeexample}
    %
    It may be advisable to use |fixed zerofill| and/or |sci zerofill| to force
    at least one digit after the decimal separator to improve placement of
    exponents:
    %
\begin{codeexample}[]
% requires \usepackage{array}
\pgfplotstabletypeset[
    use comma,
    columns={dof,error1,error2,info,{grad(log(dof),log(error2))}},
    columns/error1/.style={dec sep align,sci zerofill},
    columns/error2/.style={sci,sci subscript,sci zerofill,dec sep align},
    columns/info/.style={fixed,dec sep align},
    columns/{grad(log(dof),log(error2))}/.style={fixed,dec sep align,fixed zerofill}
]
    {pgfplotstable.example1.dat}
\end{codeexample}

    The style |dec sep align| actually introduces two new |tabular|
    columns,\footnote{Unfortunately, \texttt{dec sep align} is currently not
    very flexible when it comes to column type modifications. In particular, it
    is not possible to use colored columns or cells in conjunction with
    \texttt{dec sep align}. The \texttt{\textbackslash rowcolor} command works
    properly; the color hangover introduced by \texttt{colortbl} is adjusted
    automatically.} namely |r@{}l|. It introduces multicolumns for column
    names accordingly and handles numbers which do not have a decimal
    separator.

    Note that for fixed point numbers, it might be an alternative to use
    |fixed zerofill| combined with |column type=r| to get a similar effect.

    Please note that this style overwrites |column type|, |assign cell content|
    and some number formatting settings.
\end{stylekey}

%--------------------------------------------------
% FIXME : doesn't really work as intended:
% \begin{stylekey}{/pgfplots/table/dec sep align/no unbounded}
%     Changes the internal processing of |dec sep align| such that unbounded values like $NaN$ and $\pm \infty$ will be aligned in exactly the same way as the column name.
%
%     This avoids funny spacing around unbounded coordinates when used with |dec sep align|.

% NO GALLERY
% \begin{codeexample}[]
% \pgfplotstabletypeset{pgfplotstable.example4.dat}
% \vrule
%
% \pgfplotstabletypeset[
%     columns/b/.style={fixed,precision=1},
% ]
%     {pgfplotstable.example4.dat}
% \vrule
%
% \pgfplotstabletypeset[
%     columns/b/.style={fixed,precision=1,dec sep align},
% ]
%     {pgfplotstable.example4.dat}
% \vrule
%
% \pgfplotstabletypeset[
%     columns/b/.style={fixed,precision=1,dec sep align,dec sep align/no unbounded},
% ]
%     {pgfplotstable.example4.dat}
% \end{codeexample}
% \end{stylekey}
%--------------------------------------------------

\begin{stylekey}{/pgfplots/table/sci sep align=\marg{header column type} (initially c)}
    A style which aligns numerical columns at the exponent in scientific
    representation.

    The first argument determines the alignment of the header column.

    It works similarly to |dec sep align|, namely by introducing two
    artificial columns |r@{}l| for alignment.

    Please note that you need |\usepackage{array}| for this style.

    Please note that this style overwrites |column type|, |assign cell content|
    and some number formatting settings.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/dcolumn=\marg{tabular column type}\marg{type for column name} (initially \{D\{.\}\{.\}\{2\}\}\{c\})}
    A style which can be used together with the |dcolumn| package of David
    Carlisle. It also enables alignment at the decimal separator. However, the
    decimal separator needs to be exactly one character which is incompatible
    with `|{,}|' (the default setting for |use comma|).
\end{stylekey}

\begin{pgfplotskey}{table/sort=\marg{true,false} (initially false)}
    If set to |true|, |\pgfplotstabletypeset| will sort the table before
    applying its operation.

    See the description of |\pgfplotstablesort| for how to configure |sort key|
    and |sort cmp|.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    sort,sort key=error2,
    columns={dof,error1,error2},
    columns/error1/.style={sci,sci subscript,sci zerofill,dec sep align},
    columns/error2/.style={sci,sci subscript,sci zerofill,dec sep align},
]
    {pgfplotstable.example1.dat}
\end{codeexample}

    The |sort| mechanism is applied before the actual typesetting routine
    starts, i.e.\@ it has the same effect as if you'd call |\pgfplotstablesort|
    manually before typesetting the table (however, the |sort| key has the
    advantage of respecting the |include outfiles| caching mechanism). Any
    |create on use| specifications are resolved before calling the |sort key|.

    %The |sort| key applies also to |\addplot table[sort,read completely]|.
\end{pgfplotskey}

\begin{stylekey}{/pgfplots/table/every first column}
    A style which is installed for every first column only.
    %
\begin{codeexample}[narrow]
\pgfplotstabletypeset[
 every head row/.style={before row=\hline,after row=\hline\hline},
 every last row/.style={after row=\hline},
 every first column/.style={
  column type/.add={|}{}
 },
 every last column/.style={
  column type/.add={}{|}
 }]
    {pgfplotstable.example1.dat}
\end{codeexample}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every last column}
    A style which is installed for every last column only.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every even column}
    A style which is installed for every column with even column index
    (starting with~$0$).
{
\pgfplotstableset{
    columns={dof,error1,{grad(log(dof),log(error2))},info},
    columns/error1/.style={
        column name=$L_2$,
        sci,sci zerofill,sci subscript,
        precision=3},
    columns/dof/.style={
        int detect,
        column name=\textsc{Dof}},
    columns/{grad(log(dof),log(error2))}/.style={
        column name=slopes $L_2$,
        fixed,fixed zerofill,
        precision=1}}

\begin{codeexample}[code only]
\pgfplotstableset{
    columns={dof,error1,{grad(log(dof),log(error2))},info},
    columns/error1/.style={
        column name=$L_2$,
        sci,sci zerofill,sci subscript,
        precision=3},
    columns/dof/.style={
        int detect,
        column name=\textsc{Dof}},
    columns/{grad(log(dof),log(error2))}/.style={
        column name=slopes $L_2$,
        fixed,fixed zerofill,
        precision=1}}
\end{codeexample}

\begin{codeexample}[narrow,graphic=white]
% requires \usepackage{colortbl}
\pgfplotstabletypeset[
 every even column/.style={
  column type/.add={>{\columncolor[gray]{.8}}}{}
}]
    {pgfplotstable.example1.dat}
\end{codeexample}
}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every column}
    A style which is applied to every column.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    every column/.code={
        \ifnum\pgfplotstablecol>0
            \pgfkeysalso{column type/.add={|}{}}%
        \fi
    },
]
{
first second third
1 2 3
4 5 6
}
\end{codeexample}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every odd column}
    A style which is installed for every column with odd column index (starting
    with~$0$).
\end{stylekey}

\begin{command}{\pgfplotstablecol}
    During the evaluation of row or column options, this command expands to the
    current column's index.
\end{command}

\begin{command}{\pgfplotstablecolname}
    During the evaluation of column options, this command expands to the
    current column's name. It is valid while |\pgfplotstabletypeset| processes
    the column styles (including the preprocessing step explained in
    Section~\ref{sec:pgfplotstable:preproc}), prepares the output cell content
    and checks row predicates.
\end{command}

\begin{command}{\pgfplotstablerow}
\label{pgfplotstable:page:tablerow}
    During the evaluation of row or column options, this command expands to the
    current row's index.

    ``Evaluation of column options'' applies to any of the styles in
    Section~\ref{sec:data:processing}, i.e.\@ preprocessing, typesetting, and
    postprocessing.

    The macro |\pgfplotstablerow| can take any of the values $0,1,2,\dotsc,n-1$
    where $n$ is the value of |\pgfplotstablerows|.

    ``Evaluation of row options'' applies to stuff like |every last row|.

    Note that it will have the special value $-1$ for the header row.
\end{command}

\begin{command}{\pgfplotstablecols}
    During the evaluation of row or column options, this command expands to the
    total number of columns in the output table.
\end{command}

\begin{command}{\pgfplotstablerows}
    During evaluation of \emph{columns}, this command expands to the total
    number of \emph{input} rows. You can use it inside of |row predicate|.

    During evaluation of \emph{rows}, this command expands to the total number
    of \emph{output} rows.
\end{command}

\begin{command}{\pgfplotstablename}
    During |\pgfplotstabletypeset|, this macro contains the table's macro name
    as top-level expansion. If you are unfamiliar with ``top-level-expansions''
    and `|\expandafter|', you will probably never need this macro.

    Advances users may benefit from expressions like

    |\expandafter\pgfplotstabletypeset\pgfplotstablename|.

    For tables which have been loaded from disk (and have no explicitly
    assigned macro name), this expands to a temporary macro.
\end{command}


\subsection{Configuring Row Appearance: Styles}

The following styles allow to configure the final table code \emph{after any
cell contents have been assigned}.

\begin{key}{/pgfplots/table/before row=\marg{\TeX{} code}}
    Contains \TeX{} code which will be installed before the first cell in a
    row.

    Keep in mind that \PGFPlotstable{} does no magic -- it is simply a code
    generator which produces |tabular| environments. Consequently, you can add
    any \TeX{} code which you would normally write into your |tabular|
    environment here.

    An example could be a multicolumn heading for which \PGFPlotstable{} has no
    own solution:
    %
\begin{codeexample}[]
% \usepackage{booktabs}
\pgfplotstabletypeset[
    column type=l,
    every head row/.style={
        before row={
            \toprule
            & \multicolumn{2}{c}{Singular} & \multicolumn{2}{c}{Plural}\\
        },
        after row=\midrule,
    },
    every last row/.style={
        after row=\bottomrule},
    columns/person/.style       ={column name=},
    columns/singGaeilge/.style  ={column name=Gaeilge},
    columns/pluralGaeilge/.style={column name=Gaeilge},
    columns/singEnglish/.style  ={column name=English},
    columns/pluralEnglish/.style={column name=English},
    col sep=&,row sep=\\,
    string type,
]{
person & singEnglish  & singGaeilge & pluralEnglish  & pluralGaeilge\\
1st    & at me        & agam        & at us          & againn\\
2st    & at you       & agat        & at you         & agaibh\\
3st    & at him       & aige        & at them        & acu\\
       & at her       & aici        &                &\\
}
\end{codeexample}
%
    \noindent The example declares a lot of options and is finally followed by
    a short inline table. The |every head row| style configures |\multicolumn|
    headings by means of verbatim |tabular| code, together with |booktabs|
    rules. It might be helpful to consider the |debug| or |outfile| keys during
    experiments. The |columns/...| styles are necessary to change the column
    headings.

    Sometimes, one wants to combine |\multicolumn| and |\rowcolor|. From what I
    know about \LaTeX{}, this is a little bit complicated: it requires the use of
    |\columncolor| inside of the |\multicolumn|. As in the example above, it is
    necessary to modify the code generated by \PGFPlotstable{} a little bit.
    Keep in mind that \PGFPlotstable{} is just a code generator for |tabular|
    environments -- modify whatever you want. The following example
    demonstrates the combination of |\multicolumn| and |\rowcolor|. It has been
    taken out of an -- admittedly advanced -- application:
    %
\begin{codeexample}[]
\newcolumntype{C}{>{\centering\arraybackslash}p{6mm}}% a centered fixed-width-column
\pgfplotstabletypeset[
    col sep=&,
    row sep=\\,
    every head row/.style={
    % as in the previous example, this patches the first row:
        before row={
            \hline
            \rowcolor{lightgray}
            \multicolumn{3}{|>{\columncolor{lightgray}}c|}{Quantenzahlen} & Term-\\
            \rowcolor{lightgray}
        },
        after row=\hline,
    },
    every last row/.style={
        after row=\hline},
    % define column-specific styles:
    columns/n/.style={column type=|C,column name=$n$},
    columns/l/.style={column type=|C,column name=$\ell$},
    columns/lambda/.style={column type=|C,column name=$\lambda$},
    columns/text/.style={column type=|c|,column name=bezeichnung,
        string type % <-it contains formatted data
    },
] {
n & l & lambda & text\\
1 & 0 & 0 & $1 s\sigma$ \\
2 & 0 & 0 & $2 s\sigma$ \\
2 & 1 & 0 & $2 p\sigma$ \\
2 & 1 & 1 & $2 p \pi $\\
3 & 2 & 0 & $3 d\sigma$ \\
3 & 2 & 2 & $3 d\delta$ \\
}
\end{codeexample}

    Up to the number formatting (which actually invokes |\pgfmathprintnumber|),
    the code above is equivalent to the listing
    %
\begin{codeexample}[code only]
\newcolumntype{C}{>{\centering\arraybackslash}p{6mm}}% a centered fixed-width-column
\begin{tabular}{|C|C|C|c|}
\hline
\rowcolor{lightgray} \multicolumn{3}{|>{\columncolor{lightgray}}c|}{Quantenzahlen} & Term-\\
\rowcolor{lightgray} $n$ & $\ell$ & $\lambda$ & bezeichnung\\
\hline
$1$ & $0$ & $0$ & $1 s\sigma$ \\
$2$ & $0$ & $0$ & $2 s\sigma$ \\
$2$ & $1$ & $0$ & $2 p\sigma$ \\
$2$ & $1$ & $1$ & $2 p \pi$ \\
$3$ & $2$ & $0$ & $3 d\sigma$ \\
$3$ & $2$ & $2$ & $3 d\delta$ \\
\hline
\end{tabular}
\end{codeexample}

    Clearly, the overhead introduced by defining a lot of styles is only worth
    the effort if you require number printing, automated processing, or have a
    huge bulk of similar tables.
\end{key}

\begin{key}{/pgfplots/table/after row=\marg{\TeX{} code}}
    Contains \TeX{} code which will be installed after the last cell in a row
    (i.e.\@ after |\\|).
\end{key}

\begin{stylekey}{/pgfplots/table/every even row}
    A style which is installed for each row with even row index. The first row
    is supposed to be a ``head'' row and does not count. Indexing starts
    with~$0$.
{
\pgfplotstableset{
    columns={dof,error1,{grad(log(dof),log(error2))}},
    columns/error1/.style={
        column name=$L_2$,
        sci,sci zerofill,sci subscript,
        precision=3},
    columns/dof/.style={
        int detect,
        column name=\textsc{Dof}},
    columns/{grad(log(dof),log(error2))}/.style={
        column name=slopes $L_2$,
        fixed,fixed zerofill,
        precision=1},
}

\begin{codeexample}[code only]
\pgfplotstableset{
    columns={dof,error1,{grad(log(dof),log(error2))}},
    columns/error1/.style={
        column name=$L_2$,
        sci,sci zerofill,sci subscript,
        precision=3},
    columns/dof/.style={
        int detect,
        column name=\textsc{Dof}},
    columns/{grad(log(dof),log(error2))}/.style={
        column name=slopes $L_2$,
        fixed,fixed zerofill,
        precision=1}}
\end{codeexample}

\begin{codeexample}[narrow,graphic=white]
% requires \usepackage{booktabs}
\pgfplotstabletypeset[
    every head row/.style={
        before row=\toprule,after row=\midrule},
    every last row/.style={
        after row=\bottomrule},
]
    {pgfplotstable.example1.dat}
\end{codeexample}

\begin{codeexample}[narrow,graphic=white]
% requires \usepackage{booktabs,colortbl}
\pgfplotstabletypeset[
    every even row/.style={
        before row={\rowcolor[gray]{0.9}}},
    every head row/.style={
        before row=\toprule,after row=\midrule},
    every last row/.style={
        after row=\bottomrule},
]
    {pgfplotstable.example1.dat}
\end{codeexample}
}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every odd row}
    A style which is installed for each row with odd row index. The first row
    is supposed to be a ``head'' row and does not count. Indexing starts
    with~$0$.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every head row}
    A style which is installed for each first row in the tabular. This can be
    used to adjust options for column names or to add extra lines/colors.

\begin{codeexample}[]
\pgfplotstabletypeset[
  % suppress the header row 'col1  col2  col3':
  every head row/.style={output empty row},
  col sep=comma,
  columns/col1/.style={string type,column type=r},
  columns/col2/.style={string type,column type=l},
  columns/col3/.style={string type,column type=l},
  ]
{
    col1,col2,col3
    Col A,B,C
    The first column,E,F
}
\end{codeexample}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every first row}
    A style which is installed for each first \emph{data} row, i.e.\@ after the
    head row.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every last row}
    A style which is installed for each last row.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every row no \meta{index}}
    A style which is installed for the row with index \meta{index}.
\end{stylekey}

\begin{keylist}{%
    /pgfplots/table/every nth row=\marg{integer}\marg{options},
    /pgfplots/table/every nth row=\marg{integer\oarg{shift}}\marg{options}%
}
    This allows to install \meta{options} for every $n$th row with
    $n=$\meta{integer}.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    every nth row={3}{before row=\midrule},
    every head row/.style={
        before row=\toprule,after row=\midrule},
    every last row/.style={
        after row=\bottomrule},
]{
    a b
    0 0
    1 1
    2 2
    3 3
    4 4
    5 5
    6 6
    7 7
    8 8
}
\end{codeexample}
    %
    Only data rows are considered for |every nth row|; it will never apply to
    column names and data rows are numbered like $i=0,1,2,\dotsc$ (the example
    above applies it to the rows with $a = 3,6$). Since the case $i=0$ can be
    handled by |every first row|, it is not considered for |every nth row|.

    The second syntax allows to provide an additional \meta{shift}:
\begin{codeexample}[]
\pgfplotstabletypeset[
    every nth row={3[+1]}{before row=\midrule},
]{
    a b
    0 0
    1 1
    2 2
    3 3
    4 4
    5 5
    6 6
    7 7
    8 8
    9 9
    10 10
}
\end{codeexample}
    %
    \noindent Here, the style is applied to rows $i=1,4,7,10$ (mathematically,
    it is applied if $(i \mod n) = $\meta{shift}). The \meta{shift} can
    be negative.

    You can define many |every nth row| styles, they are processed in the order
    of occurrence (consider using |before row/.add=|\marg{before
    existing}\marg{after existing} to modify an existing value).

    Note that |every nth row/.style 2 args=...| is the same as
    |every nth row=...|.
\end{keylist}

\begin{stylekey}{/pgfplots/table/output empty row}
    A style which suppresses output for the current row.

    This style is evaluated very late, after all column-specific content
    modifications have been applied. It is equivalent to
    %
\begin{codeexample}[code only]
\pgfplotstableset{
    output empty row/.style={
        typeset cell/.style={@cell content={}}
    },
}
\end{codeexample}

    See |every head row| for an application.
\end{stylekey}


\subsection{Configuring Single Cell Appearance: Styles}

Besides the possibilities to change column styles and row styles, there are
also a couple of styles to change single cells.

\begin{stylekey}{/pgfplots/table/every row \meta{rowindex} column \meta{colindex}}
    A style which applies to at most one cell: the one with row index
    \meta{rowindex} and column index \meta{colindex}. Each of these indices
    starts with~$0$.

    The style is evaluated in the same context as the |preproc cell content|,
    |assign cell content|, and |postproc cell content| keys and it is a
    legitimate possibility to modify any of these parameters. It is also
    possible to replace the initial cell value by assigning something to
    |@cell content|.

    For example, consider this unmodified table:
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    col sep=&,row sep=\\]{
  colA & colB & colC \\
  11   & 12   & 13   \\
  21   & 22   & 23   \\
}
\end{codeexample}

    Now, we change the number format of one of its cells, and at the same time
    we change the formatting of another (single) cell:
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    every row 1 column 2/.style={/pgf/number format/sci},
    every row 0 column 0/.style={postproc cell content/.style={@cell content=\textbf{##1}}},
    col sep=&,row sep=\\]{
  colA & colB & colC \\
  11   & 12   & 13   \\
  21   & 22   & 23   \\
}
\end{codeexample}
    Note that this style is (only) applied to input row/column values.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every row no \meta{rowindex} column no \meta{colindex}}
    This is actually the same -- |row no| and |row| are both supported, the
    same for |column| and |column no|.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/every row \meta{rowindex} column \meta{colname}}
    A similar style as above, but it allows column \emph{names} rather than
    column indices. Column names need to be provided in the same way as for
    other column-specific styles (including the extra curly braces in case
    \meta{colname} contains special characters).

    Our example from above can thus become:
\begin{codeexample}[]
\pgfplotstabletypeset[
    every row 1 column colB/.style={string replace*={2}{4}},
    every row 0 column colA/.style={preproc/expr={##1*8}},
    col sep=&,row sep=\\]{
  colA & colB & colC \\
  11   & 12   & 13   \\
  21   & 22   & 23   \\
}
\end{codeexample}
    The example employs the |string replace*| preprocessor style and the
    |preproc/expr| style. All preprocessor or postprocessor styles can be used.

    Please refer to Section~\ref{sec:data:processing} for predefined choices.
\end{stylekey}


\subsection{Customizing and Getting the Tabular Code}

The following keys allow changes of alignment (|begin table|) and |font| and
they allow to write the generated code to |outfile|s (see also
|write to macro|). Furthermore, the generated code can be fine--tuned to
provide other sorts of table output, beyond \LaTeX{}.

\begin{stylekey}{/pgfplots/table/every table=\marg{file name}}
    A style which is installed at the beginning of every
    |\pgfplotstabletypeset| command.\footnote{The \texttt{every table} style is
    installed \emph{after} options provided to \texttt{\textbackslash
    pgfplotstabletypeset}; it has higher precedence.}

    The table file name is given as first argument.
\end{stylekey}

\begin{key}{/pgfplots/table/font=\marg{font name} (initially empty)}
    Assigns a font used for the complete table.
\end{key}

\begin{key}{/pgfplots/table/begin table=\marg{code} (initially \textbackslash begin\{tabular\})}
    Contains \marg{code} which is generated as table start.

    The following example uses a |longtable| instead\index{longtable} of
    |tabular|:
    %
\begin{codeexample}[code only]
\pgfplotstableset{
    begin table=\begin{longtable},
    end table=\end{longtable},
}
\end{codeexample}

    Note that |longtable| allows the use of \emph{replicated headers} for
    multi-page tables\index{Multi-page} by means of its
    \declareandlabel{\endhead} macro:\index{Replicate headers}
    %
\begin{codeexample}[code only]
% replicate column names on top of every page of a multi-page table:
\pgfplotstableset{
    row sep=\\,
    begin table=\begin{longtable},
    end table=\end{longtable},
    every head row/.append style={after row=\endhead},
}
\end{codeexample}

    If the first page should have a different header, you can use
    \declareandlabel{\endfirsthead} provided by the |longtable| package:
    %
\begin{codeexample}[code only]
% replicate column names on top of every page of a multi-page table,
% but with different values for first page:
\pgfplotstableset{
    row sep=\\,
    begin table=\begin{longtable},
    end table=\end{longtable},
    every head row/.append style={after row={%
            \caption{The caption}%
            \endfirsthead
            \multicolumn{3}{c}{{\bfseries \tablename\ \thetable{} -- continued from previous page}} \\
            \endhead
        },
    },
}
\end{codeexample}
    %
    \noindent The preceding example uses the |longtable| macros |\caption|,
    |\endfirsthead|, |\thetable|, and |\endhead|. In addition, it requires to
    provide the number of columns (|{3}| in this case) \emph{explicitly}.

    It is also possible to \emph{change} the value of |begin table|. For
    example,
\begin{codeexample}[code only]
\pgfplotstableset{
    begin table/.add={}{[t]},
}
\end{codeexample}
    %
    prepends the empty string |{}| and appends the prefix |[t]|. Thus,
    `|\begin{tabular}|' becomes `|\begin{tabular}[t]|'.
\end{key}

\begin{key}{/pgfplots/table/end table=\marg{code} (initially \textbackslash end\{tabular\})}
    Contains \meta{code} which is generated as table end.
\end{key}

\begin{codekey}{/pgfplots/table/typeset cell}
    A code key which assigns \declareandlabel{/pgfplots/table/@cell content} to
    the final output of the current cell.

    The first argument, |#1|, is the final cell's value. After this macro, the
    value of |@cell content| will be written to the output.

    The default implementation is
    %
\begin{codeexample}[code only]
/pgfplots/table/typeset cell/.code={%
    \ifnum\c@pgfplotstable@colindex=\c@pgfplotstable@numcols\relax
        \pgfkeyssetvalue{/pgfplots/table/@cell content}{#1\\}%
    \else
        \pgfkeyssetvalue{/pgfplots/table/@cell content}{#1&}%
    \fi
},
\end{codeexample}

    \paragraph{Attention:}

    The value of |\pgfplotstablecol| starts with $1$ in this context, i.e.\@ it
    is in the range $1,\dotsc,n$ where $n=$ |\pgfplotstablecols|. This
    simplifies checks whether we have the last column.
\end{codekey}

\begin{key}{/pgfplots/table/outfile=\marg{file name} (initially empty)}
\label{page:outfile}
    Writes the generated tabular code into \meta{file name}. It can then be
    used with |\input|\marg{file name}, \PGFPlotstable{} is no longer required
    since it contains a completely normal |tabular|.
    %
    \pgfplotstableset{begin table=\begin{tabular}}
\begin{codeexample}[]
\pgfplotstabletypeset[
    columns={dof,error1},
    outfile=pgfplotstable.example1.out.tex]
    {pgfplotstable.example1.dat}
\end{codeexample}
    %
    and |pgfplotstable.example1.out.tex| contains
    %
    %\lstdefineformat{inp}{\\\\=\string\newline}%
    \lstinputlisting[basicstyle=\ttfamily\footnotesize]{pgfplotstable.example1.out.tex}

    The command |\pgfutilensuremath| checks whether math mode is active and
    switches to math mode if necessary.\footnote{Please note that
    \lstinline{\\pgfutilensuremath} needs to be replaced by
    \lstinline{\\ensuremath} if you want to use the output file independent of
    \PGF{}. That can be done by \lstinline{\\let\\pgfutilensuremath=\\ensuremath}
    which enables the \LaTeX{} command \lstinline{\\ensuremath}.}
\end{key}

\begin{key}{/pgfplots/table/include outfiles=\marg{boolean} (initially false)}
    If enabled, any already existing outfile will be |\input| instead of
    overwritten.
    %
\begin{codeexample}[code only]
\pgfplotstableset{include outfiles} % for example in the document's preamble
\end{codeexample}
    %
    This allows to place any corrections manually into generated output files
    since \PGFPlotstable{} won't overwrite the resulting tables automatically.

    This will affect tables for which the |outfile| option is set. If you wish
    to apply it to every table, consider
    %
\begin{codeexample}[code only]
\pgfplotstableset{every table/.append style={outfile={#1.out}}}
\end{codeexample}
    %
    \noindent which will generate an |outfile| name for every table.
\end{key}

\begin{key}{/pgfplots/table/force remake=\marg{boolean} (initially false)}
    If enabled, the effect of |include outfiles| is disabled. As all key
    settings only last until the next brace (or |\end|\meta{}), this key can be
    used to regenerate some output files while others are still included.
\end{key}

\begin{key}{/pgfplots/table/write to macro=\marg{\textbackslash macroname}}
    If the value of |write to macro| is not empty, the completely generated
    (tabular) code will be written into the macro \meta{\textbackslash
    macroname}.

    See the |typeset=false| key in case you need \emph{only} the resulting
    macro.
\end{key}

\begin{key}{/pgfplots/table/skip coltypes=\mchoice{true,false} (initially false)}
    Allows to skip the \meta{coltypes} in |\begin{tabular}|\marg{coltypes}.
    This allows simplifications for other table types which don't have \LaTeX's
    table format.
\end{key}

\begin{key}{/pgfplots/table/typeset=\mchoice{true,false} (initially true)}
    A boolean which disables the final typesetting stage. Use |typeset=false|
    in conjunction with |write to macro| if only the generated code is of
    interest and \TeX{} should not attempt to produce any content in the output
    |pdf|.
\end{key}

\begin{key}{/pgfplots/table/debug=\marg{boolean} (initially false)}
    If enabled, it will write every final tabular code to your logfile.
\end{key}

\begin{key}{/pgfplots/table/TeX comment=\marg{comment sign} (initially \%)}
    The comment sign which is inserted into outfiles to suppress trailing white
    space.
\end{key}

\noindent As a last example, we use \PGFPlotstable{} to write an |.html| file
(including number formatting and rounding!):
%
% \usepackage{listings}
\begin{codeexample}[width=8cm]
\pgfplotstabletypeset[
    begin table={<table>}, end table={</table>},
    typeset cell/.style={
      /pgfplots/table/@cell content={<td>#1</td>}
    },
    before row=<tr>,after row=</tr>,
    skip coltypes, typeset=false,
    verbatim,% configures number printer
    TeX comment=,
    columns={level,dof,error1},
    outfile=pgfplotstable.example1.out.html,
]{pgfplotstable.example1.dat}
\lstinputlisting
    [basicstyle=\ttfamily\footnotesize]
    {pgfplotstable.example1.out.html}
\end{codeexample}


\subsection{Defining Column Types for \texttt{tabular}}

Besides input of text files, it is sometimes desirable to define column types
for existing \texttt{tabular} environments.

\begin{command}{\newcolumntype\marg{letter}\oarg{number of
    arguments}$>$\marg{before column}\meta{column type}$<$\marg{after column}
}
    The command |\newcolumntype| is part of the |array| package and it defines
    a new column type \meta{letter} for use in \LaTeX{} tabular environments.
    %
\begin{codeexample}[code only]
\usepackage{array}
\end{codeexample}

\begin{codeexample}[]
\newcolumntype{d}{>{-}c<{+}}
\begin{tabular}{dl}
a & b \\
c & d \\
\end{tabular}
\end{codeexample}

    Now, the environment |pgfplotstablecoltype| can be used in \meta{before
    column} and \meta{after column} to define numerical columns:
    %
% \usepackage{array}
\begin{codeexample}[]
% requires \usepackage{array}
\newcolumntype{L}[1]
    {>{\begin{pgfplotstablecoltype}[#1]}r<{\end{pgfplotstablecoltype}}}

\begin{tabular}{L{int detect}L{sci,sci subscript,sci zerofill}}
9      & 2.50000000e-01\\
25     & 6.25000000e-02\\
81     & 1.56250000e-02\\
289    & 3.90625000e-03\\
1089   & 9.76562500e-04\\
4225   & 2.44140625e-04\\
16641  & 6.10351562e-05\\
66049  & 1.52587891e-05\\
263169 & 3.81469727e-06\\
1050625& 9.53674316e-07\\
\end{tabular}
\end{codeexample}
    %
    \noindent The environment |pgfplotstablecoltype| accepts an optional
    argument which may contain any number formatting options. It is an error if
    numerical columns contain non-numerical data, so it may be necessary to use
    |\multicolumn| for column names.
    %
\begin{codeexample}[]
% requires \usepackage{array}
\newcolumntype{L}[1]
    {>{\begin{pgfplotstablecoltype}[#1]}r<{\end{pgfplotstablecoltype}}}

\begin{tabular}{L{int detect}L{sci,sci subscript,sci zerofill}}
\multicolumn{1}{r}{Dof} & \multicolumn{1}{r}{Error}\\
9      & 2.50000000e-01\\
25     & 6.25000000e-02\\
81     & 1.56250000e-02\\
289    & 3.90625000e-03\\
1089   & 9.76562500e-04\\
4225   & 2.44140625e-04\\
16641  & 6.10351562e-05\\
66049  & 1.52587891e-05\\
263169 & 3.81469727e-06\\
1050625& 9.53674316e-07\\
\end{tabular}
\end{codeexample}
\end{command}


\subsection{Number Formatting Options}
\label{sec:number:printing}

The following extract of \cite{tikz} explains how to configure number formats.
The common option prefix |/pgf/number format| can be omitted; it will be
recognized automatically.

All these number formatting options can also be applied to \PGFPlots{}.

\begin{command}{\pgfmathprintnumber\marg{x}}
    Generates pretty-printed output for the (real) number \meta{x}. The input
    number \meta{x} is parsed using |\pgfmathfloatparsenumber| which allows
    arbitrary precision.

    Numbers are typeset in math mode using the current set of number printing
    options, see below. Optional arguments can also be provided using
    |\pgfmathprintnumber[|\meta{options}|]|\marg{x}.
\end{command}

\begin{command}{\pgfmathprintnumberto\marg{x}\marg{\textbackslash macro}}
    Returns the resulting number into \meta{\textbackslash macro} instead of
    typesetting it directly.
\end{command}

\begin{key}{/pgf/number format/fixed}
    Configures |\pgfmathprintnumber| to round the number to a fixed number of
    digits after the period, discarding any trailing zeros.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,fixed,precision=2}
\pgfmathprintnumber{4.568}\hspace{1em}
\pgfmathprintnumber{5e-04}\hspace{1em}
\pgfmathprintnumber{0.1}\hspace{1em}
\pgfmathprintnumber{24415.98123}\hspace{1em}
\pgfmathprintnumber{123456.12345}
\end{codeexample}

    See Section~\ref{sec:number:styles} for how to change the appearance.
\end{key}

\begin{key}{/pgf/number format/fixed zerofill=\marg{boolean}  (default true)}
    Enables or disables zero filling for any number drawn in fixed point
    format.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2}
\pgfmathprintnumber{4.568}\hspace{1em}
\pgfmathprintnumber{5e-04}\hspace{1em}
\pgfmathprintnumber{0.1}\hspace{1em}
\pgfmathprintnumber{24415.98123}\hspace{1em}
\pgfmathprintnumber{123456.12345}
\end{codeexample}
    %
    This key affects numbers drawn with |fixed| or |std| styles (the latter
    only if no scientific format is chosen).
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,std,fixed zerofill,precision=2}
\pgfmathprintnumber{4.568}\hspace{1em}
\pgfmathprintnumber{5e-05}\hspace{1em}
\pgfmathprintnumber{1}\hspace{1em}
\pgfmathprintnumber{123456.12345}
\end{codeexample}

    See Section~\ref{sec:number:styles} for how to change the appearance.
\end{key}

\begin{key}{/pgf/number format/sci}
    Configures |\pgfmathprintnumber| to display numbers in scientific format,
    that means sign, mantissa and exponent (base~$10$). The mantissa is rounded
    to the desired |precision| (or |sci precision|, see below).
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,sci,precision=2}
\pgfmathprintnumber{4.568}\hspace{1em}
\pgfmathprintnumber{5e-04}\hspace{1em}
\pgfmathprintnumber{0.1}\hspace{1em}
\pgfmathprintnumber{24415.98123}\hspace{1em}
\pgfmathprintnumber{123456.12345}
\end{codeexample}

    See Section~\ref{sec:number:styles} for how to change the exponential
    display style.
\end{key}

\begin{key}{/pgf/number format/sci zerofill=\marg{boolean}  (default true)}
    Enables or disables zero filling for any number drawn in scientific format.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,sci,sci zerofill,precision=2}
\pgfmathprintnumber{4.568}\hspace{1em}
\pgfmathprintnumber{5e-04}\hspace{1em}
\pgfmathprintnumber{0.1}\hspace{1em}
\pgfmathprintnumber{24415.98123}\hspace{1em}
\pgfmathprintnumber{123456.12345}
\end{codeexample}
    %
    As with |fixed zerofill|, this option does only affect numbers drawn in
    |sci| format (or |std| if the scientific format is chosen).

    See Section~\ref{sec:number:styles} for how to change the exponential
    display style.
\end{key}

\begin{stylekey}{/pgf/number format/zerofill=\marg{boolean} (default true)}
    Sets both |fixed zerofill| and |sci zerofill| at once.
\end{stylekey}

\begin{keylist}{/pgf/number format/std,%
    /pgf/number format/std=\meta{lower e},
    /pgf/number format/std=\meta{lower e}:\meta{upper e}%
}
    Configures |\pgfmathprintnumber| to a standard algorithm. It chooses either
    |fixed| or |sci|, depending on the order of magnitude. Let $n=s \cdot m
    \cdot 10^e$ be the input number and $p$ the current precision. If $-p/2 \le
    e \le 4$, the number is displayed using |fixed| format. Otherwise, it is
    displayed using |sci| format.

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,std,precision=2}
\pgfmathprintnumber{4.568}\hspace{1em}
\pgfmathprintnumber{5e-04}\hspace{1em}
\pgfmathprintnumber{0.1}\hspace{1em}
\pgfmathprintnumber{24415.98123}\hspace{1em}
\pgfmathprintnumber{123456.12345}
\end{codeexample}
    %
    The parameters can be customized using the optional integer argument(s): if
    $\text{\meta{lower e}} \le e \le \text{\meta{upper e}}$, the number is
    displayed in |fixed| format, otherwise in |sci| format. Note that
    \meta{lower e} should be negative for useful results. The precision used
    for scientific format can be adjusted with |sci precision| if necessary.

\end{keylist}

\begin{keylist}{/pgf/number format/relative*=\meta{exponent base 10}}
    Configures |\pgfmathprintnumber| to format numbers relative to an order of
    magnitude, $10^r$, where $r$ is an integer number.

    This key addresses different use-cases.


    \paragraph{First use-case:}

    provide a unified format for a \emph{sequence} of numbers. Consider the
    following test:
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/relative*={1}}
\pgfmathprintnumber{6.42e-16}\hspace{1em}
\pgfmathprintnumber{1.2}\hspace{1em}
\pgfmathprintnumber{6}\hspace{1em}
\pgfmathprintnumber{20.6}\hspace{1em}
\pgfmathprintnumber{87}
\end{codeexample}
    %
    \noindent With any other style, the |6.42e-16| would have been formatted as
    an isolated number. Here, it is rounded to |0| because when viewed relative
    to $10^1$ (the exponent $1$ is the argument for |relative|), it has no
    significant digits.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/relative*={2}}
\pgfmathprintnumber{123.345}\hspace{1em}
\pgfmathprintnumber{0.0012}\hspace{1em}
\pgfmathprintnumber{0.0014}\hspace{1em}
\end{codeexample}
    %
    \noindent The example above applies the initial |precision=2| to |123.345|
    -- relative to $100$. Two significant digits of |123.345| relative to $100$
    are |123|. Note that the ``$2$ significant digits of |123.345|'' translates
    to ``round |1.2345| to $2$ digits'', which would yield |1.2300|. Similarly,
    the other two numbers are |0| compared to $100$ using the given
    |precision|.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/relative*={-3}}
\pgfmathprintnumber{123.345}\hspace{1em}
\pgfmathprintnumber{0.0012}\hspace{1em}
\pgfmathprintnumber{0.0014}\hspace{1em}
\end{codeexample}

    \paragraph{Second use-case:}

    improve rounding in the presence of \emph{inaccurate} numbers. Let us
    suppose that some limited-precision arithmetics resulted in the result
    |123456999| (like the |fpu| of \pgfname). You know that its precision is
    about five or six significant digits. And you want to provide a fixed point
    output. In this case, the trailing digits |....999| are a numerical
    artifact due to the limited precision. Use |relative*=3,precision=0| to
    eliminate the artifacts:
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,relative*={3},precision=0}
\pgfmathprintnumber{123456999}\hspace{1em}
\pgfmathprintnumber{123456999.12}
\end{codeexample}
    %
    \noindent Here, |precision=0| means that we inspect |123456.999| and round
    that number to $0$ digits. Finally, we move the period back to its initial
    position. Adding |relative style=fixed| results in fixed point output
    format:
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,relative*={3},precision=0,relative style=fixed}
\pgfmathprintnumber{123456999}\hspace{1em}
\pgfmathprintnumber{123456999.12}
\end{codeexample}
    %
    \noindent Note that there is another alternative for this use-case which is
    discussed later: the |fixed relative| style.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,fixed relative,precision=6}
\pgfmathprintnumber{123456999}\hspace{1em}
\pgfmathprintnumber{123456999.12}
\end{codeexample}

    You might wonder why there is an asterisk in the key's name. The short
    answer is: there is also a \declareandlabel{/pgf/number format/relative}
    number printer which does unexpected things. The key |relative*| repairs
    this. Existing code will still use the old behavior.

    Technically, the key works as follows: as already explained above,
    |relative*=3| key applied to |123456999.12| moves the period by three
    positions and analyzes |123456.99912|. Mathematically speaking, we are
    given a number $x = \pm m \cdot 10^e$ and we attempt to apply
    |relative*=|$r$. The method then rounds $x / 10^r$ to |precision| digits.
    Afterwards, it multiplies the result by $10^r$ and typesets it.
\end{keylist}

\begin{stylekey}{/pgf/number format/every relative}
    A style which configures how the |relative| method finally displays its
    results.

    The initial configuration is
    %
\begin{codeexample}[code only]
\pgfkeys{/pgf/number format/every relative/.style=std}
\end{codeexample}

    Note that rounding is turned off when the resulting style is being
    evaluated (since |relative| already rounded the number).

    Although supported, I discourage from using |fixed zerofill| or
    |sci zerofill| in this context -- it may lead to a suggestion of higher
    precision than is actually used (because |fixed zerofill| might simply add
    |.00| although there was a different information before |relative| rounded
    the result).
\end{stylekey}

\begin{key}{/pgf/number format/relative style=\marg{options}}
    The same as |every relative/.append style=|\marg{options}.
\end{key}

\begin{keylist}{/pgf/number format/fixed relative}
    Configures |\pgfmathprintnumber| to format numbers in a similar way to the
    |fixed| style, but the |precision| is interpreted relatively to the
    number's exponent.

    The motivation is to get the same rounding effect as for |sci|, but to
    display the number in the |fixed| style:
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,fixed relative,precision=3}
\pgfmathprintnumber{1000.0123}\hspace{1em}
\pgfmathprintnumber{100.0567}\hspace{1em}
\pgfmathprintnumber{0.000010003452}\hspace{1em}
\pgfmathprintnumber{0.010073452}\hspace{1em}
\pgfmathprintnumber{1.23567}\hspace{1em}
\pgfmathprintnumber{1003.75}\hspace{1em}
\pgfmathprintnumber{1006.75}\hspace{1em}
\end{codeexample}

    The effect of |fixed relative| is that the number is rounded to
    \emph{exactly} the first \meta{precision} non-zero digits, no matter how
    many leading zeros the number might have.

    Use |fixed relative| if you want |fixed| and if you know that only the
    first $n$ digits are correct. Use |sci| if you need a scientific display
    style and only the first $n$ digits are correct.

    Note that |fixed relative| ignores the |fixed zerofill| flag.

    See also the |relative*| key. Note that the |relative=|\marg{exponent} key
    explicitly moves the period to some designated position before it attempts
    to round the number. Afterwards, it ``rounds from the right'', i.e.\@ it
    rounds to that explicitly chosen digit position. In contrast to that,
    |fixed relative| ``rounds from the left'': it takes the \emph{first}
    non-zero digit, temporarily places the period after this digit, and rounds
    that number. The rounding style |fixed| leaves the period where it is, and
    rounds everything behind that digit. The |sci| style is similar to
    |fixed relative|.
\end{keylist}

\begin{key}{/pgf/number format/int detect}
    Configures |\pgfmathprintnumber| to detect integers automatically. If the
    input number is an integer, no period is displayed at all. If not, the
    scientific format is chosen.

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,int detect,precision=2}
\pgfmathprintnumber{15}\hspace{1em}
\pgfmathprintnumber{20}\hspace{1em}
\pgfmathprintnumber{20.4}\hspace{1em}
\pgfmathprintnumber{0.01}\hspace{1em}
\pgfmathprintnumber{0}
\end{codeexample}
\end{key}

\begin{command}{\pgfmathifisint\marg{number constant}\marg{true code}\marg{false code}}
    A command which does the same check as |int detect|, but it invokes
    \meta{true code} if the \meta{number constant} actually is an integer and
    the \meta{false code} if not.

    As a side-effect, |\pgfretval| will contain the parsed number, either in
    integer format or as parsed floating point number.

    The argument \meta{number constant} will be parsed with
    |\pgfmathfloatparsenumber|.
\begin{codeexample}[]
15 \pgfmathifisint{15}{is an int: \pgfretval.}{is no int}\hspace{1em}
15.5 \pgfmathifisint{15.5}{is an int: \pgfretval.}{is no int}
\end{codeexample}
\end{command}

\begin{key}{/pgf/number format/int trunc}
    Truncates every number to integers (discards any digit after the period).
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,int trunc}
\pgfmathprintnumber{4.568}\hspace{1em}
\pgfmathprintnumber{5e-04}\hspace{1em}
\pgfmathprintnumber{0.1}\hspace{1em}
\pgfmathprintnumber{24415.98123}\hspace{1em}
\pgfmathprintnumber{123456.12345}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/frac}
    Displays numbers as fractionals.
    %
\begin{codeexample}[width=3cm]
\pgfkeys{/pgf/number format/frac}
\pgfmathprintnumber{0.333333333333333}\hspace{1em}
\pgfmathprintnumber{0.5}\hspace{1em}
\pgfmathprintnumber{2.133333333333325e-01}\hspace{1em}
\pgfmathprintnumber{0.12}\hspace{1em}
\pgfmathprintnumber{2.666666666666646e-02}\hspace{1em}
\pgfmathprintnumber{-1.333333333333334e-02}\hspace{1em}
\pgfmathprintnumber{7.200000000000000e-01}\hspace{1em}
\pgfmathprintnumber{6.666666666666667e-02}\hspace{1em}
\pgfmathprintnumber{1.333333333333333e-01}\hspace{1em}
\pgfmathprintnumber{-1.333333333333333e-02}\hspace{1em}
\pgfmathprintnumber{3.3333333}\hspace{1em}
\pgfmathprintnumber{1.2345}\hspace{1em}
\pgfmathprintnumber{1}\hspace{1em}
\pgfmathprintnumber{-6}
\end{codeexample}

    \begin{key}{/pgf/number format/frac TeX=\marg{\textbackslash macro} (initially \texttt{\textbackslash frac})}
        Allows to use a different implementation for |\frac| inside of the
        |frac| display type.
    \end{key}

    \begin{key}{/pgf/number format/frac denom=\meta{int} (initially empty)}
        Allows to provide a custom denominator for |frac|.
        %
\begin{codeexample}[width=3cm]
\pgfkeys{/pgf/number format/.cd,frac, frac denom=10}
\pgfmathprintnumber{0.1}\hspace{1em}
\pgfmathprintnumber{0.5}\hspace{1em}
\pgfmathprintnumber{1.2}\hspace{1em}
\pgfmathprintnumber{-0.6}\hspace{1em}
\pgfmathprintnumber{-1.4}\hspace{1em}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/number format/frac whole=\mchoice{true,false} (initially true)}
        Configures whether complete integer parts shall be placed in front of
        the fractional part. In this case, the fractional part will be less
        then $1$. Use |frac whole=false| to avoid whole number parts.
        %
\begin{codeexample}[width=3cm]
\pgfkeys{/pgf/number format/.cd,frac, frac whole=false}
\pgfmathprintnumber{20.1}\hspace{1em}
\pgfmathprintnumber{5.5}\hspace{1em}
\pgfmathprintnumber{1.2}\hspace{1em}
\pgfmathprintnumber{-5.6}\hspace{1em}
\pgfmathprintnumber{-1.4}\hspace{1em}
\end{codeexample}
    \end{key}

    \begin{key}{/pgf/number format/frac shift=\marg{integer} (initially 4)}
        In case you experience stability problems, try experimenting with a
        different |frac shift|. Higher shift values $k$ yield higher
        sensitivity to inaccurate data or inaccurate arithmetics.

        Technically, the following happens. If $r < 1$ is the fractional part
        of the mantissa, then a scale $i = 1/r \cdot 10^k$ is computed where
        $k$ is the shift; fractional parts of $i$ are neglected. The value
        $1/r$ is computed internally, its error is amplified.

        If you still experience stability problems, use |\usepackage{fp}| in
        your preamble. The |frac| style will then automatically employ the
        higher absolute precision of |fp| for the computation of $1/r$.
    \end{key}
\end{key}

\begin{key}{/pgf/number format/precision=\marg{number}}
    Sets the desired rounding precision for any display operation. For
    scientific format, this affects the mantissa.
\end{key}

\begin{key}{/pgf/number format/sci precision=\meta{number or empty} (initially empty)}
    Sets the desired rounding precision only for |sci| styles.

    Use |sci precision={}| to restore the initial configuration (which uses the
    argument provided to |precision| for all number styles).
\end{key}

\begin{key}{/pgf/number format/read comma as period=\mchoice{true,false} (initially false)}
    This is one of the few keys which allows to customize the number parser. If
    this switch is turned on, a comma is read just as a period.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/read comma as period}
\pgfmathprintnumber{1234,56}
\end{codeexample}
    %
    This is typically undesired as it can cause side-effects with math parsing
    instructions. However, it is supported to format input numbers or input
    tables. Consider |use comma| to typeset the result with a comma as well.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    read comma as period,
    use comma}
\pgfmathprintnumber{1234,56}
\end{codeexample}

    \paragraph{Note:}

    this key requires a \pgfname\ version which is more recent
    than~\pgfname~3.0.0.
\end{key}


\subsubsection{Changing Number Format Display Styles}%
\label{sec:number:styles}

You can change the way how numbers are displayed. For example, if you use the
`\texttt{fixed}' style, the input number is rounded to the desired precision
and the current fixed point display style is used to typeset the number. The
same is applied to any other format: first, rounding routines are used to get
the correct digits, afterwards a display style generates proper \TeX{}-code.

\begin{key}{/pgf/number format/set decimal separator=\marg{text}}
    Assigns \meta{text} as decimal separator for any fixed point number
    (including the mantissa in sci format).
\end{key}

\begin{key}{/pgf/number format/dec sep=\marg{text}}
    Just another name for |set decimal separator|.
\end{key}

\begin{key}{/pgf/number format/set thousands separator=\marg{text}}
    Assigns \meta{text} as thousands separator for any fixed point number
    (including the mantissa in sci format).
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,
    fixed zerofill,
    precision=2,
    set thousands separator={}}
\pgfmathprintnumber{1234.56}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,
    fixed zerofill,
    precision=2,
    set thousands separator={}}
\pgfmathprintnumber{1234567890}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,
    fixed zerofill,
    precision=2,
    set thousands separator={.}}
\pgfmathprintnumber{1234567890}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,
    fixed zerofill,
    precision=2,
    set thousands separator={,}}
\pgfmathprintnumber{1234567890}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,
    fixed zerofill,
    precision=2,
    set thousands separator={{{{,}}}}}
\pgfmathprintnumber{1234567890}
\end{codeexample}
    %
    The last example employs commas and disables the default comma-spacing.
\end{key}

\begin{key}{/pgf/number format/1000 sep=\marg{text}}
    Just another name for |set thousands separator|.
\end{key}

\begin{key}{/pgf/number format/1000 sep in fractionals=\marg{boolean} (initially false)}
    Configures whether the fractional part should also be grouped into groups
    of three digits.

    The value |true| will activate the |1000 sep| for both integer and
    fractional parts. The value |false| will activate |1000 sep| only for the
    integer part.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,
    precision=999,
    set thousands separator={\,},
    1000 sep in fractionals,
}
\pgfmathprintnumber{1234.1234567}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,fixed zerofill,
    precision=9,
    set thousands separator={\,},
    1000 sep in fractionals,
}
\pgfmathprintnumber{1234.1234567}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/min exponent for 1000 sep=\marg{number} (initially 0)}
    Defines the smallest exponent in scientific notation which is required to
    draw thousand separators. The exponent is the number of digits minus one,
    so $\meta{number}=4$ will use thousand separators starting with $1e4 =
    10000$.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    int detect,
    1000 sep={\,},
    min exponent for 1000 sep=0}
\pgfmathprintnumber{5000}; \pgfmathprintnumber{1000000}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    int detect,
    1000 sep={\,},
    min exponent for 1000 sep=4}
\pgfmathprintnumber{1000}; \pgfmathprintnumber{5000}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    int detect,
    1000 sep={\,},
    min exponent for 1000 sep=4}
\pgfmathprintnumber{10000}; \pgfmathprintnumber{1000000}
\end{codeexample}
    %
    \noindent A value of |0| disables this feature (negative values are
    ignored).
\end{key}


\begin{key}{/pgf/number format/use period}
    A predefined style which installs periods `\texttt{.}' as decimal
    separators and commas `\texttt{,}' as thousands separators. This style is
    the default.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,fixed,precision=2,use period}
\pgfmathprintnumber{12.3456}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,fixed,precision=2,use period}
\pgfmathprintnumber{1234.56}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/use comma}
    A predefined style which installs commas `\texttt{,}' as decimal separators
    and periods `\texttt{.}' as thousands separators.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,fixed,precision=2,use comma}
\pgfmathprintnumber{12.3456}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,fixed,precision=2,use comma}
\pgfmathprintnumber{1234.56}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/skip 0.=\marg{boolean} (initially false)}
    Configures whether numbers like $0.1$ shall be typeset as $.1$ or not.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,
    fixed zerofill,precision=2,
    skip 0.}
\pgfmathprintnumber{0.56}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,
    fixed,
    fixed zerofill,precision=2,
    skip 0.=false}
\pgfmathprintnumber{0.56}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/showpos=\marg{boolean} (initially false)}
    Enables or disables display of plus signs for non-negative numbers.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/showpos}
\pgfmathprintnumber{12.345}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/showpos=false}
\pgfmathprintnumber{12.345}
\end{codeexample}

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,showpos,sci}
\pgfmathprintnumber{12.345}
\end{codeexample}
\end{key}

\begin{stylekey}{/pgf/number format/print sign=\marg{boolean}}
    A style which is simply an alias for |showpos=|\meta{boolean}.
\end{stylekey}

\begin{key}{/pgf/number format/sci 10e}
    Uses $m \cdot 10^e$ for any number displayed in scientific format.

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,sci,sci 10e}
\pgfmathprintnumber{12.345}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/sci 10\textasciicircum e}
    The same as `|sci 10e|'.
\end{key}

\begin{key}{/pgf/number format/sci e}
    Uses the `$1e{+}0$' format which is generated by common scientific tools
    for any number displayed in scientific format.

\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,sci,sci e}
\pgfmathprintnumber{12.345}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/sci E}
    The same with an uppercase `\texttt{E}'.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,sci,sci E}
\pgfmathprintnumber{12.345}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/sci subscript}
    Typesets the exponent as subscript for any number displayed in scientific
    format. This style requires very little space.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,sci,sci subscript}
\pgfmathprintnumber{12.345}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/sci superscript}
    Typesets the exponent as superscript for any number displayed in scientific
    format. This style requires very little space.
    %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/.cd,sci,sci superscript}
\pgfmathprintnumber{12.345}
\end{codeexample}
\end{key}

\begin{key}{/pgf/number format/sci generic=\marg{keys}}
    Allows to define a custom number style for the scientific format. Here,
    \meta{keys} can be one of the following choices (omit the long key prefix):

    \begin{key}{/pgf/number format/sci generic/mantissa sep=\marg{text} (initially empty)}
        Provides the separator between the mantissa and the exponent. It might
        be |\cdot|, for example,
    \end{key}

    \begin{key}{/pgf/number format/sci generic/exponent=\marg{text} (initially empty)}
        Provides text to format the exponent. The actual exponent is available
        as argument |#1| (see below).
    \end{key}

\begin{codeexample}[]
\pgfkeys{
    /pgf/number format/.cd,
    sci,
    sci generic={mantissa sep=\times,exponent={10^{#1}}}}
\pgfmathprintnumber{12.345};
\pgfmathprintnumber{0.00012345}
\end{codeexample}
    %
    The \meta{keys} can depend on three parameters, namely on |#1| which is the
    exponent, |#2| containing the flags entity of the floating point number and
    |#3| is the (unprocessed and unformatted) mantissa.

    Note that |sci generic| is \emph{not} suitable to modify the appearance of
    fixed point numbers, nor can it be used to format the mantissa (which is
    typeset like fixed point numbers). Use |dec sep|, |1000 sep| and
    |print sign| to customize the mantissa.
\end{key}

\begin{key}{/pgf/number format/retain unit mantissa=\mchoice{true,false} (initially true)}
    Allows to omit a unit mantissa.
    %
\begin{codeexample}[]
\pgfkeys{
    /pgf/number format/.cd,
    sci, retain unit mantissa=false}
\pgfmathprintnumber{10.5};
\pgfmathprintnumber{10};
\pgfmathprintnumber{1010};
\pgfmathprintnumber[precision=1]{-1010};
\end{codeexample}
    %
    The feature is applied after rounding to the desired precision: if the
    remaining mantissa is equal to~$1$, it will be omitted. It applies to all
    styles involving the scientific format (including |std|).
\end{key}

\begin{key}{/pgf/number format/@dec sep mark=\marg{text}}
    Will be placed right before the place where a decimal separator belongs to.
    However, \meta{text} will be inserted even if there is no decimal
    separator. It is intended as place-holder for auxiliary routines to find
    alignment positions.

    This key should never be used to change the decimal separator! Use
    |dec sep| instead.
\end{key}

\begin{key}{/pgf/number format/@sci exponent mark=\marg{text}}
    Will be placed right before exponents in scientific notation. It is
    intended as place-holder for auxiliary routines to find alignment
    positions.

    This key should never be used to change the exponent!
\end{key}

\begin{key}{/pgf/number format/assume math mode=\marg{boolean} (default true)}
    Set this to |true| if you don't want any checks for math mode.

    The initial setting installs a |\pgfutilensuremath| around each final
    number to change to math mode if necessary. Use |assume math mode=true| if
    you know that math mode is active and you don't want |\pgfutilensuremath|.
\end{key}

\begin{stylekey}{/pgf/number format/verbatim}
    A style which configures the number printer to produce verbatim text
    output, i.e.\@ it doesn't contain \TeX{} macros.
    %
\begin{codeexample}[]
\pgfkeys{
    /pgf/fpu,
    /pgf/number format/.cd,
    sci,
    verbatim}
\pgfmathprintnumber{12.345};
\pgfmathprintnumber{0.00012345};
\pgfmathparse{exp(15)}
\pgfmathprintnumber{\pgfmathresult}
\end{codeexample}
    %
    The style resets |1000 sep|, |dec sep|, |print sign|, |skip 0.| and sets
    |assume math mode|. Furthermore, it installs a |sci generic| format for
    verbatim output of scientific numbers.

    However, it will still respect |precision|, |fixed zerofill|,
    |sci zerofill| and the overall styles |fixed|, |sci|, |int detect| (and
    their variants). It might be useful if you intend to write output files.
\end{stylekey}


\section{From Input Data To Output Tables: Data Processing}
\label{sec:data:processing}

The conversion from an unprocessed input table to a final typesetted |tabular|
code uses four stages for every cell,
%
\begin{enumerate}
    \item Loading the table,
    \item Preprocessing,
    \item Typesetting,
    \item Postprocessing.
\end{enumerate}
%
The main idea is to select one typesetting algorithm (for example ``format my
numbers with the configured number style''). This algorithm usually doesn't
need to be changed. Fine-tuning can then be done using zero, one or more
preprocessors and postprocessors. Preprocessing can mean to select only
particular rows or to apply some sort of operation before the typesetting
algorithm sees the content. Postprocessing means to apply fine-tuning to the
resulting \TeX{} output -- for example to deal with empty cells or to insert
unit suffixes or modify fonts for single cells.

Note that this kind of operation is processed column by column. As a
consequence, the keys for preprocessing, typesetting, and postprocessing apply
to styles on columns. They are unavailable for row styles like
|every last row|. If you need to apply such content-based operations on
specific rows, you have to write code of sorts ``if |\pgfplotstablerow| $=$
generate content differently''.


\subsection{Loading the table}

This first step to typeset a table involves the obvious input operations.
Furthermore, the ``new column creation'' operations explained in
Section~\ref{pgfplotstable:createcol} are processed at this time. The table
data is read (or acquired) as already explained earlier in this manual. Then,
if columns are missing, column alias and |create on use| specifications will be
processed as part of the loading procedure. See
Section~\ref{pgfplotstable:createcol} for details about column creation.


\subsection{Typesetting Cell Content}

Typesetting cells means to take their value and ``do something''. In many
cases, this involves number formatting routines. For example, the ``raw'' input
data |12.56| might become |1.26| |\cdot| |10^1|. The result of this stage is no
longer useful for content-based computations. The typesetting step follows the
preprocessing step.

Typesetting cell content is applied in a column by column fashion, i.e.\@ it
can be configured for row styles. See the notes in the introduction of
Section~\ref{sec:data:processing} for details how to apply such styles on
specific rows only.

\begin{codekey}{/pgfplots/table/assign cell content}
    Allows to redefine the algorithm which assigns cell contents. The argument
    |#1| is the (unformatted) contents of the input table.

    The resulting output needs to be written to
    |/pgfplots/table/@cell content|.
    %
\pgfplotstableset{
    %debug=true,
    begin table=\begin{tabular},% eliminate the '[b]' from the preamble here
}
% \usepackage{booktabs}
% \usepackage{multirow}
\begin{codeexample}[]
% An example how to use
% \usepackage{multirow} and
% \usepackage{booktabs}:
\pgfplotstabletypeset[
    columns/Z/.style={
        column name={},
        assign cell content/.code={% use \multirow for Z column:
            \ifnum\pgfplotstablerow=0
                \pgfkeyssetvalue{/pgfplots/table/@cell content}
                    {\multirow{4}{*}{##1}}%
            \else
                \pgfkeyssetvalue{/pgfplots/table/@cell content}{}%
            \fi
        },
    },
    % use \booktabs as well (compare examples above):
    every head row/.style={before row=\toprule,after row=\midrule},
    every last row/.style={after row=\bottomrule},
    row sep=\\,col sep=&,
    outfile=pgfplotstable.multirow.out,% write it to file
]{% here: inline data in tabular format:
    Z    & a & b \\
    data & 1 & 2 \\
         & 3 & 4 \\
         & 5 & 6 \\
         & 7 & 8 \\
}
% ... and show the generated file:
\lstinputlisting[basicstyle=\footnotesize\ttfamily]{pgfplotstable.multirow.out}
\end{codeexample}
        \index{multirow}%
    %
    \noindent The example above uses |\usepackage{multirow}| to format column
    |Z|. More precisely, it uses |\multirow{4}{*}{data}| for row \#0 of column
    |Z| and the empty string for any other row in column |Z|.

    Please note that you may need special attention for |#1=|\marg{}, i.e.\@
    the empty string. This may happen if a column has less rows than the first
    column. \PGFPlotstable{} will balance columns automatically in this case,
    inserting enough empty cells to match the number of rows of the first
    column.

    Please note further that if any column has more entries than the first
    column, these entries will be skipped and a warning message will be issued
    into the logfile.

    This key is evaluated inside of a local \TeX{} group, so any local macro
    assignments will be cleared afterwards.
\end{codekey}

\begin{stylekey}{/pgfplots/table/numeric type}
    A style which (re)defines |assign cell content| back to its original value
    which assumes numerical data.

    It invokes |\pgfmathprintnumberto| and writes the result into
    |@cell content|.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/string type}
    A style which redefines |assign cell content| to simply return the ``raw''
    input data, that means as text column. This assumes input tables with valid
    \LaTeX{} content (verbatim printing is not supported).
\end{stylekey}

\begin{stylekey}{/pgfplots/table/verb string type}
    A style which redefines |assign cell content| to return the ``raw'' as is.
    Thus, it is quite similar to |string type| -- but it will return control
    sequences and (many, not all) special characters without expanding them.

    You may need to combine |verb string type| with |special chars|.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/numeric as string type}
    A style which redefines |assign cell content| such that it assumes
    numerical input data. It returns a string literal describing the input
    number either as integer or in scientific (exponential) notation. In
    contrast to |numeric type|, it does not apply number formatting.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/date type=\marg{date format}}% (initially \year-\month-\day)}
    A style which expects ISO dates of the form |YYYY-MM-DD| in each cell and
    produces pretty-printed strings on output. The output format is given as
    \meta{date format}. Inside of \meta{date format}, several macros which are
    explained below can be used.
    %
% \usepackage{pgfcalendar}
\begin{codeexample}[]
% Requires
% \usepackage{pgfcalendar}
\pgfplotstableset{columns={date,account1}}

% plotdata/accounts.dat contains:
%
% date              account1  account2  account3
% 2008-01-03        60        1200      400
% 2008-02-06        120       1600      410
% 2008-03-15        -10       1600      410
% 2008-04-01        1800      500       410
% 2008-05-20        2300      500       410
% 2008-06-15        800       1920      410

% Show the contents in `string type':
\pgfplotstabletypeset[
    columns/date/.style={string type}
]{plotdata/accounts.dat}
\hspace{1cm}
% Show the contents in `date type':
\pgfplotstabletypeset[
    columns/date/.style={date type={\monthname\ \year}}
]{plotdata/accounts.dat}
\end{codeexample}
    %
    This style \textbf{requires} to load the \PGF{} \textbf{calendar package}:
    %
\begin{codeexample}[code only]
\usepackage{pgfcalendar}
\end{codeexample}

    \begin{command}{\year}
        Inside of \meta{date format}, this macro expands to the year as a
        number (like |2008|).
    \end{command}

    \begin{command}{\month}
        Inside of \meta{date format}, this macro expands to the month as a
        number, starting with~$1$ (like |1|).
    \end{command}

    \begin{command}{\monthname}
        Inside of \meta{date format}, this macro expands to the month's name as
        set in the current language (like |January|). See below for how to
        change the language.
    \end{command}

    \begin{command}{\monthshortname}
        Inside of \meta{date format}, this macro expands to the month's short
        name as set in the current language (like |Jan|). See below for how to
        change the language.
    \end{command}

    \begin{command}{\day}
        Inside of \meta{date format}, this macro expands to the day as number
        (like |31|).
    \end{command}

    \begin{command}{\weekday}
        Inside of \meta{date format}, this macro expands to the weekday number
        ($0$ for Monday, $1$ for Tuesday etc.).
    \end{command}

    \begin{command}{\weekdayname}
        Inside of \meta{date format}, this macro expands to the weekday's name
        in the current language (like |Wednesday|). See below for how to change
        the language.
    \end{command}

    \begin{command}{\weekdayshortname}
        Inside of \meta{date format}, this macro expands to the weekday's short
        name in the current language (like |Wed|). See below for how to change
        the language.
    \end{command}


    \subsubsection*{Changing the language for dates}

    The date feature is implemented using the \PGF{} calendar module. This
    module employs the package |translator| (if it is loaded). I don't have
    more details yet, sorry. Please refer to \cite{tikz} for more details.
\end{stylekey}


\subsection{Preprocessing Cell Content}
\label{sec:pgfplotstable:preproc}

The preprocessing step allows to change cell contents \emph{before} any
typesetting routine (like number formatting) has been applied. Thus, if tables
contain numerical data, it is possible to apply math operations at this stage.
Furthermore, cells can be erased depending on their numerical value. The
preprocessing step follows after the data acquisition step (``loading step'').
This means in particular that you can create (or copy) columns and apply
operations on them.

Preprocessing is applied in a column by column fashion, i.e.\@ it can be
configured for row styles. See the notes in the introduction of
Section~\ref{sec:data:processing} for details how to apply such styles on
specific rows only.

\begin{codekey}{/pgfplots/table/preproc cell content}
    Allows to \emph{modify} the contents of cells \emph{before}
    |assign cell content| is called.

    The semantics is as follows: before the preprocessor, |@cell content|
    contains the raw input data (or, maybe, the result of another preprocessor
    call). After the preprocessor, |@cell content| is filled with a -- possibly
    modified -- value. The resulting value is then used as input to
    |assign cell content|.

    In the default settings, |assign cell content| expects numerical input. So,
    the preprocessor is expected to produce numerical output.

    It is possible to provide multiple preprocessor directives using
    |/.append code| or |/.append style| key handlers.

    In case you don't want (or need) stackable preprocessors, you can also use
    `|#1|' to get the raw input datum as it is found in the file. Furthermore,
    the key |@unprocessed cell content| will also contain the raw input datum.
\end{codekey}

\begin{stylekey}{/pgfplots/table/string replace=\marg{cell match}\marg{cell replacement}}
    Appends code to the current |preproc cell content| value which replaces any
    cell with exact match \meta{cell match} by \meta{cell replacement}. No
    expansion is performed during this step; \meta{cell match} must match
    literally.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[columns={level,dof}]
    {pgfplotstable.example1.dat}

\pgfplotstabletypeset[
    columns={level,dof},
    columns/level/.style={string replace={A}{B}}, % does nothing because there is no cell 'A'
    columns/dof/.style={string replace={256}{-42}}]  % replace cell '256' with '-42'
    {pgfplotstable.example1.dat}
\end{codeexample}

    See the |string replace*| method for sub-string replacement.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/string replace*=\marg{pattern}\marg{replacement}}
    Appends code to the current |preproc cell content| value which replaces
    every occurrence of \meta{pattern} with \meta{replacement}. No expansion is
    performed during this step; \meta{pattern} must match literally.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    string replace*={2}{6},
    col sep=&,row sep=\\]{
  colA & colB & colC \\
  11   & 12   & 13   \\
  21   & 22   & 23   \\
}
\end{codeexample}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/clear infinite}
    Appends code to the current |preproc cell content| value which replaces
    every infinite number with the empty string. This clears any cells with
    $\pm \infty$ and NaN.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/preproc/expr=\marg{math expression}}
    Appends code to the current |preproc cell content| value which evaluates
    \meta{math expression} for every cell. Arithmetics are carried out in
    floating point.

    Inside of \meta{math expression}, use one of the following expressions to
    get the current cell's value.
    %
    \begin{itemize}
        \item The string `|##1|' expands to the cell's content as it has been
            found in the input file, ignoring preceding preprocessors.

            This is usually enough.
        \item The command |\thisrow|\marg{the currently processed column
            name} expands to the current cell's content. This will also
            include the results of preceding preprocessors.

            Note that |\thisrow{}| in this context (inside of the
            preprocessor) is not as powerful as in the context of column
            creation routines: the argument must match exactly the name of
            the currently processed column name. You can also use the
            shorthand

            |\thisrow{\pgfplotstablecolname}|.

        \item The command |\pgfkeysvalueof{/pgfplots/table/@cell content}| is
            the same.
    \end{itemize}
    %
\begin{codeexample}[]
\pgfplotstabletypeset[
    columns={level},
    columns/level/.style={
        column name={$2\cdot \text{level}+4$},
        preproc/expr={2*##1 + 4}
    }
]
    {pgfplotstable.example1.dat}
\end{codeexample}

    Empty cells won't be processed, assuming that a math expression with an
    ``empty number'' will fail.

    Note that there is also an |create col/expr| which is more powerful than
    |preproc/expr|.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/multiply by=\marg{real number}}
    Appends code to the current |preproc cell content| value which multiplies
    every cell by \meta{real number}. Arithmetics are carried out in floating
    point.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/divide by=\marg{real number}}
    Appends code to the current |preproc cell content| value which divides
    every cell by \meta{real number}. Arithmetics are carried out in floating
    point.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/sqrt}
    Appends code to the current |preproc cell content| value which takes the
    square root $\sqrt{\cdot}$ of every non-empty cell. Arithmetics are carried
    out in floating point.

    The following example copies the column |error1| and applies |sqrt| to the
    copy.
    %
\begin{codeexample}[]
\pgfplotstableset{
    columns={error1,sqrterror1},
    create on use/sqrterror1/.style={create col/copy=error1},
    columns/error1/.style={column name=$\epsilon$},
    columns/sqrterror1/.style={sqrt,column name=$\sqrt \epsilon$},
    sci,sci 10e,precision=3,sci zerofill
}
\pgfplotstabletypeset{pgfplotstable.example1.dat}
\end{codeexample}
    %
    Please take a look at Section~\ref{pgfplotstable:createcol} for details
    about |create on use|.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/multiply -1}
    Appends code to current |preproc cell content| value which multiplies every
    cell by $-1$. This style does the same job as |multiply by=-1|, it is just
    faster because only the sign changes.
    %
\begin{codeexample}[]
\pgfplotstableset{
    columns={dof,error2,slopes2},
    columns/error2/.style={sci,sci zerofill},
    columns/slopes2/.style={dec sep align,empty cells with={\ensuremath{-}}},
    create on use/slopes2/.style=
        {create col/gradient loglog={dof}{error2}}}

\pgfplotstabletypeset{pgfplotstable.example1.dat}

\pgfplotstabletypeset[columns/slopes2/.append style={multiply -1}]
    {pgfplotstable.example1.dat}
\end{codeexample}
\end{stylekey}

\begin{codekey}{/pgfplots/table/row predicate}
    A boolean predicate which allows to select particular rows of the input
    table, based on the current row's index. The argument |#1| contains the
    current row's index (starting with~$0$, not counting comment lines or
    column names).

    The return value is assigned to the \TeX{}-if
    \declareandlabel{\ifpgfplotstableuserow}. If the boolean is not changed,
    the return value is true.
    %
\begin{codeexample}[newline=]
% requires \usepackage{booktabs}
\pgfplotstabletypeset[
    every head row/.style={
        before row=\toprule,after row=\midrule},
    every last row/.style={
        after row=\bottomrule},
    row predicate/.code={%
        \ifnum#1>4\relax
            \ifnum#1<8\relax
                \pgfplotstableuserowfalse
            \fi
        \fi}
]
    {pgfplotstable.example1.dat}
\end{codeexample}
    %
    Please note that |row predicate| is applied \emph{before} any other option
    which affects row (or column) appearance. It is evaluated before
    |assign cell content|. One of the consequences is that even/odd row styles
    refer to those rows for which the predicate returns |true|. In fact, you
    can use |row predicate| to truncate the complete table before it has
    actually been processed.

    During |row predicate|, the macro |\pgfplotstablerows| contains the total
    number of \emph{input} rows.

    Furthermore, |row predicate| applies only to the typeset routines, not the
    read methods. If you want to plot only selected table entries with
    |\addplot table|, use the \PGFPlots{} coordinate filter options.
\end{codekey}

\begin{stylekey}{/pgfplots/table/skip rows between index=\marg{begin}\marg{end}}
    A style which appends a |row predicate| which discards selected rows. The
    selection is done by index where indexing starts with~$0$. Every row with
    index $\meta{begin} \le i < \meta{end}$ will be skipped.
    %
\begin{codeexample}[narrow]
% requires \usepackage{booktabs}
\pgfplotstabletypeset[
    every head row/.style={
        before row=\toprule,after row=\midrule},
    every last row/.style={
        after row=\bottomrule},
    skip rows between index={2}{4},
    skip rows between index={7}{9}
]
    {pgfplotstable.example1.dat}
\end{codeexample}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/select equal part entry of=\marg{part no}\marg{part count}}
    A style which overwrites |row predicate| with a subset selection predicate.
    The idea is to split the current column into \meta{part count} equally
    sized parts and select only \meta{part no}.

    This can be used to simulate multicolumn tables.
    %
\begin{codeexample}[]
% requires \usepackage{booktabs}
\pgfplotstableset{
    every head row/.style={before row=\toprule,after row=\midrule},
    every last row/.style={after row=\bottomrule}}

\pgfplotstabletypeset[string type]{pgfplotstable.example2.dat}%
~
\pgfplotstabletypeset[
    columns={A,B,A,B},
    display columns/0/.style={select equal part entry of={0}{2},string type},% first part of `A'
    display columns/1/.style={select equal part entry of={0}{2},string type},% first part of `B'
    display columns/2/.style={select equal part entry of={1}{2},string type},% second part of `A'
    display columns/3/.style={select equal part entry of={1}{2},string type},% second part of `B'
]
    {pgfplotstable.example2.dat}
\end{codeexample}
    %
    The example above shows the original file as-is on the left side. The right
    side shows columns A,B,A,B -- but only half of the elements are shown,
    selected by indices \#0 or \#1 of \#2. The parts are equally large, up to a
    remainder.

    If the available number of rows is not divisible by \meta{part count}, the
    remaining entries are distributed equally among the first parts.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/unique=\marg{column name}}
    A style which appends a |row predicate| which suppresses successive
    occurrences of the same elements in \meta{column name}. For example, if
    \meta{column name} contains |1,1,3,5,5,6,5,0|, the application of |unique|
    results in |1,3,5,6,5,0| (the last |5| is kept -- it is not directly
    preceded by another |5|).

    The algorithm uses string token comparison to find multiple
    occurrence.\footnote{To be more precise, the comparison is done using
    \texttt{\textbackslash ifx}, i.e.\@ cell contents won't be expanded. Only
    the tokens as they are seen in the input table will be used.}

    The argument \meta{column name} can be a column name, index, alias, or
    |create on use| specification (the latter one must not depend on other
    |create on use| statements). It is not necessary to provide a \meta{column
    name} which is part of the output.

    However, it \emph{is} necessary that the |unique| predicate can be
    evaluated for all columns, starting with the first one. That means it is an
    error to provide |unique| somewhere deep in column-specific styles.
\end{stylekey}


\subsection{Postprocessing Cell Content}

The postprocessing step is applied after the typesetting stage. Its main
purpose is to apply final formatting instructions which are not content-based.

Postprocessing is applied in a column by column fashion, i.e.\@ it can be
configured for row styles. See the notes in the introduction of
Section~\ref{sec:data:processing} for details how to apply such styles on
specific rows only.

\begin{codekey}{/pgfplots/table/postproc cell content}
    Allows to \emph{modify} assigned cell content \emph{after} it has been
    assigned, possibly content-dependent. Ideas could be to draw negative
    numbers in red, typeset single entries in bold face or insert replacement
    text.

    This key is evaluated \emph{after} |assign cell content|. Its semantics is
    to modify an existing |@cell content| value.

    There may be more than one |postproc cell content| command, if you use
    |/.append code| or |/.append style| to define them:
    %
\begin{codeexample}[]
% requires \usepackage{eurosym}
\pgfplotstabletypeset[
    column type=r,
    columns={dof,info},
    columns/info/.style={
        % stupid example for multiple postprocessors:
        postproc cell content/.append style={
            /pgfplots/table/@cell content/.add={$\bf}{$},
        },
        postproc cell content/.append style={
            /pgfplots/table/@cell content/.add={}{\EUR{}},
        }
    }]
    {pgfplotstable.example1.dat}
\end{codeexample}
    %
    The code above modifies |@cell content| in two steps. The net effect is to
    prepend ``|$\bf |'' and to append ``|$ \EUR|''. It should be noted that
    |pgfkeys| handles |/.style| and |/.code| in (basically) the same way --
    both are simple code keys and can be used as such. You can combine both
    with |/.append style| and |/.append code|. Please refer to~\cite[section
    about pgfkeys]{tikz} for details.

    As in |assign cell content|, the code can evaluate helper macros like
    |\pgfplotstablerow| to change only particular entries. Furthermore, the
    postprocessor may depend on the unprocessed cell input (as it has been
    found in the input file or produced by the loading procedure) and/or the
    preprocessed cell value. These values are available as
    %
    \begin{itemize}
        \item the key \declareandlabel{@unprocessed cell content} which
            stores the raw input,
        \item the key \declareandlabel{@cell content after rowcol styles}
            which stores the value of |@cell content| after evaluating cell
            specific styles,
        \item the key \declareandlabel{@preprocessed cell content} which
            stores the result of the preprocessor,
        \item the key \declareandlabel{@cell content} which contains the
            result of the typesetting routine,
        \item the shorthand `|#1|' which is also the unprocessed input
            argument as it has been found in the input table.
    \end{itemize}
    %
    Remember that you can access the key values using

    |\pgfkeysvalueof{/pgfplots/table/@preprocessed cell content}|

    at any time.

    This allows complete context-based formatting options. Please remember that
    empty strings may appear due to column balancing -- introduce special
    treatment if necessary.

    There is one special case which occurs if |@cell content| itself contains
    the cell separation character `|&|'. In this case, |postproc cell content|
    is invoked \emph{separately} for each part before and after the ampersand
    and the ampersand is inserted afterwards. This allows compatibility with
    special styles which create artificial columns in the output (which is
    allowed, see |dec sep align|). To allow separate treatment of each part,
    you can use the macro \declareandlabel{\pgfplotstablepartno}. It is defined
    only during the evaluation of |postproc cell content| and it evaluates to
    the current part index (starting with~$0$). If there is no ampersand in
    your text, the value will always be~$0$.

    This key is evaluated inside of a local \TeX{} group, so any local macro
    assignments will be cleared afterwards.

    The following example can be used to insert a dash, $-$, in a slope column:
    %
\begin{codeexample}[]
\pgfplotstableset{
    create on use/slopes1/.style=
        {create col/gradient loglog={dof}{error1}}}

\pgfplotstabletypeset[
    columns={dof,error1,slopes1},
    columns/error1/.style={sci,sci zerofill},
    columns/slopes1/.style={
        postproc cell content/.append code={%
            \ifnum\pgfplotstablerow=0
                \pgfkeyssetvalue{/pgfplots/table/@cell content}{\ensuremath{-}}%
            \fi
        }%
    }]
    {pgfplotstable.example1.dat}
\end{codeexample}
    %
    Since this may be useful in a more general context, it is available as
    |empty cells with| style.

    Note that header rows are now modified by this key (see
    |assign column name| if you want to modify header cell contents).
\end{codekey}

\begin{stylekey}{/pgfplots/table/empty cells with=\marg{replacement}}
    Appends code to |postproc cell content| which replaces any empty cell with
    \meta{replacement}.

    If |dec sep align| is active, the replacement will be inserted only for the
    part before the decimal separator.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/set content=\marg{content}}
    A style which redefines |postproc cell content| to always return the value
    \meta{content}.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/fonts by sign=\marg{\TeX{} code for positive}\marg{\TeX{} code for negative}}
    Appends code to |postproc cell content| which allows to set fonts for
    positive and negative numbers.

    The arguments \meta{\TeX{} code for positive} and \meta{\TeX{} code for
    negative} are inserted right before the typeset cell content. It is
    permissible to use both ways to change \LaTeX{} fonts: the
    |\textbf|\marg{argument} or the |{\bfseries |\marg{argument}|}| way.
    %

% \usepackage{pgfcalendar}
\begin{codeexample}[]
% Requires
% \usepackage{pgfcalendar}

% plotdata/accounts.dat contains:
%
% date              account1  account2  account3
% 2008-01-03        60        1200      400
% 2008-02-06        120       1600      410
% 2008-03-15        -10       1600      410
% 2008-04-01        1800      500       410
% 2008-05-20        2300      500       410
% 2008-06-15        800       1920      410

\pgfplotstabletypeset[
    columns={date,account1},
    column type=r,
    columns/date/.style={date type={\monthname\ \year}},
    columns/account1/.style={fonts by sign={}{\color{red}}}
]
    {plotdata/accounts.dat}
\end{codeexample}
    %
    In fact, the arguments for this style don't need to be font changes. The
    style |fonts by sign| inserts several braces and the matching argument into
    |@cell content|. To be more precise, it results in

    |{|\meta{\TeX{} code for negative}|{|\meta{cell value}|}}| for negative
    numbers and

    |{|\meta{\TeX{} code for positive}|{|\meta{cell value}|}}| for all other
    numbers.
\end{stylekey}


\section{Generating Data in New Tables or Columns}
\label{pgfplotstable:createcol}

It is possible to create new tables from scratch or to change tables after they
have been loaded from disk.


\subsection{Creating New Tables From Scratch}

\begin{commandlist}{%
    \pgfplotstablenew\oarg{options}\marg{row count}\marg{\textbackslash table},
    \pgfplotstablenew*\oarg{options}\marg{row count}\marg{\textbackslash table}%
}
    Creates a new table from scratch.

    The new table will contain all columns listed in the |columns| key. For
    |\pgfplotstablenew|, the |columns| key needs to be provided in
    \oarg{options}. For |\pgfplotstablenew*|, the current value of |columns| is
    used, no matter where and when it has been set.

    Furthermore, there must be |create on use| statements (see the next
    subsection) for every column which shall be generated.\footnote{Currently,
    you need to provide at least one column: the implementation gets confused
    for completely empty tables. If you do not provide any column name, a dummy
    column will be created.} Columns are generated independently, in the order
    of appearance in |columns|. As soon as a column is complete, it can be
    accessed using any of the basic level access mechanisms. Thus, you can
    build columns which depend on each other.

    The table will contain exactly \meta{row count} rows. If \meta{row count}
    is an |\pgfplotstablegetrowsof| statement, that statement will be executed
    and the resulting number of rows be used. Otherwise, \meta{row count} will
    be evaluated as number.
    %
\begin{codeexample}[]
% this key setting could be provided in the document's preamble:
\pgfplotstableset{
    % define how the 'new' column shall be filled:
    create on use/new/.style={create col/set list={4,5,6,7,...,10}}}
% create a new table with 11 rows and column 'new':
\pgfplotstablenew[columns={new}]{11}\loadedtable
% show it:
\pgfplotstabletypeset[empty cells with={---}]\loadedtable
\end{codeexample}

\begin{codeexample}[]
% create a new table with 11 rows and column 'new':
\pgfplotstablenew[
    % define how the 'new' column shall be filled:
    create on use/new/.style={create col/expr={factorial(15+\pgfplotstablerow)}},
    columns={new}]
    {11}
    \loadedtable
% show it:
\pgfplotstabletypeset\loadedtable
\end{codeexample}
\end{commandlist}

\begin{command}{\pgfplotstablevertcat\marg{\textbackslash table1}\marg{\textbackslash table2 or filename}}
\label{table:vertcat}
    Appends the contents of \meta{\textbackslash table2} to
    \meta{\textbackslash table1} (``vertical concatenation''). To be more
    precise, only columns which exist already in \meta{\textbackslash table1}
    will be appended and every column which exists in \meta{\textbackslash
    table1} must exist in \meta{\textbackslash table2} (or there must be
    |alias| or |create on use| specifications to generate them).

    If the second argument is a file name, that file will be loaded from disk.

    If \meta{\textbackslash table1} does not exist, \meta{\textbackslash
    table2} will be copied to \meta{\textbackslash table1}.
    %
\begin{codeexample}[code only]
\pgfplotstablevertcat{\output}{datafile1} % loads `datafile1' -> `\output'
\pgfplotstablevertcat{\output}{datafile2} % appends rows of datafile2
\pgfplotstablevertcat{\output}{datafile3} % appends rows of datafile3
\end{codeexample}

    \paragraph{Remark:}

    The output table \meta{\textbackslash table1} will be defined in the
    current \TeX{} scope and it will be erased afterwards. The current \TeX{}
    scope is delimited by an extra set of curly braces. However, every \LaTeX{}
    environment and, unfortunately, the \Tikz\ |\foreach| statement as well,
    introduce \TeX{} scopes.

    \PGFPlots{} has some some loop statements which do not introduce extra
    scopes. For example,
    %
\begin{codeexample}[code only]
\pgfplotsforeachungrouped \i in {1,2,...,10} {%
    \pgfplotstablevertcat{\output}{datafile\i} % appends `datafile\i' -> `\output'
}%
\end{codeexample}
    %
    These looping macros are explained in the manual of \PGFPlots{}, reference
    section ``Miscellaneous Commands''
\end{command}

\begin{command}{\pgfplotstableclear\marg{\textbackslash table}}
    Clears a table. Note that it is much more reliable to introduce extra curly
    braces `|{ ... }|' around table operations -- these braces define the scope
    of a variable (including tables).
\end{command}


\subsection{Creating New Columns From Existing Ones}

\begin{command}{\pgfplotstablecreatecol\oarg{options}\marg{new col name}\marg{\textbackslash table}}
    Creates a new column named \meta{new col name} and appends it to an already
    existing table \meta{\textbackslash table}.

    End users probably don't need to use |\pgfplotstablecreatecol| directly at
    all -- there is the high-level framework |create on use| which invokes it
    internally and can be used with simple key--value assignments (see below).
    However, this documentation explains how to use values of existing columns
    to fill new cells.

    This command offers a flexible framework to generate new columns. It has
    been designed to create new columns using the already existing values --
    for example using logical or numerical methods to combine existing values.
    It provides fast access to a row's value, the previous row's value and the
    next row's value.

    The following documentation is for everyone who wants to \emph{write}
    specialized columns. It is not particularly difficult; it is just technical
    and it requires some knowledge of |pgfkeys|. If you don't like it, you can
    resort to predefined column generation styles -- and enable those styles in
    \meta{options}.

    The column entries will be created using the command key
    \pgfmanualpdflabel{/pgfplots/table/create col/assign}{\declaretext{create col/assign}}.
    It will be invoked for every row of the table. It is supposed to assign
    contents to
    \pgfmanualpdflabel{/pgfplots/table/create col/next content}{\declaretext{create col/next content}}.
    During the evaluation, the macro |\thisrow|\marg{col name} expands to the
    current row's value of the column identified by \meta{col name}.
    Furthermore, |\nextrow|\marg{col name} expands to the \emph{next} row's
    value of the designated column and |\prevrow|\marg{col name} expands to the
    value of the \emph{previous} row.

    So, the idea is to simply redefine the command key |create col/assign| in
    such a way that it fills new cells as desired.

    Two special |assign| routines are available for the first and last row: The
    contents for the \emph{last} row is computed with
    \pgfmanualpdflabel{/pgfplots/table/create col/assign last}{\declaretext{create col/assign last}}.
    Its semantics is the same. The contents for the \emph{first} row is
    computed with
    \pgfmanualpdflabel{/pgfplots/table/create col/assign first}{\declaretext{create col/assign first}}
    to simplify special cases here. These first and last commands are optional,
    their default is to invoke the normal |assign| routine.

    The evaluation of the |assign| keys is done in local \TeX{} groups (i.e.\@
    any local definitions will be cleared afterwards).

    The following macros are useful during cell assignments:
    %
    \begin{enumerate}
        \item \declareandlabel{\prevrow}\marg{col name} /
            \declareandlabel{\getprevrow}\marg{col name}\marg{\textbackslash
            macro}

            These two routines return the value stored in the \emph{previous}
            row of the designated column \meta{col name}. The |get| routine
            stores it into \meta{\textbackslash macro}.

            The argument \meta{col name} has to denote either an existing
            column name or one for which an |alias/|\meta{col name} exists.
        \item \declareandlabel{\thisrow}\marg{col name} /
            \declareandlabel{\getthisrow}\marg{col name}\marg{\textbackslash
            macro}

            These two routines return the \emph{current} row's value stored
            in the designated column. The |get| routine stores it into
            \meta{\textbackslash macro}.

            The argument \meta{col name} has to denote either an existing
            column name or one for which an |alias/|\meta{col name} exists.
        \item \declareandlabel{\nextrow}\marg{col name} /
            \declareandlabel{\getnextrow}\marg{col name}\marg{\textbackslash
            macro}

            These two routines return the \emph{next} row's value.

            The argument \meta{col name} has to denote either an existing
            column name or one for which an |alias/|\meta{col name} exists.
        \item |\pgfplotstablerow| and |\pgfplotstablerows| which contain the
            current row's index and the total number of rows, respectively.
            See page~\pageref{pgfplotstable:page:tablerow} for details.
        \item \declareandlabel{\pgfmathaccuma} and
            \declareandlabel{\pgfmathaccumb} can be used to transport
            intermediate results. Both maintain their value from one column
            assignment to the next. All other local variables will be deleted
            after leaving the assignment routines. The initial value is the
            empty string for both of them unless they are already initialized
            by column creation styles.
        \item \declareandlabel{\pgfplotstablename} a macro containing the
            name of the currently processed table (i.e.\@ it contains the
            second argument of |\pgfplotstablecreatecol|).
        \item commands which are valid throughout every part of this package,
            for example |\pgfplotstablerow| to get the current row index or
            |\pgfplotstablerows| to get the total number of rows.
    \end{enumerate}
    %
    The \meta{col name} is expected to be a \emph{physical} column name, no
    alias or column index is allowed (unless column indices and column names
    are the same).

    The following example takes our well-known input table and creates a copy
    of the |level| column. Furthermore, it produces a lot of output to show the
    available macros. Finally, it uses |\pgfkeyslet| to assign the contents of
    the resulting |\entry| to |next content|.
    %
\begin{codeexample}[]
\pgfplotstableread{pgfplotstable.example1.dat}\loadedtable
\pgfplotstablecreatecol[
    create col/assign/.code={%
        \getthisrow{level}\entry
        \getnextrow{level}\nextentry
        \edef\entry{thisrow=\entry; nextrow=\nextentry.
            (\#\pgfplotstablerow/\pgfplotstablerows)}%
        \pgfkeyslet{/pgfplots/table/create col/next content}\entry
    }]
    {new}\loadedtable

\pgfplotstabletypeset[
    column type=l,
    columns={level,new},
    columns/new/.style={string type}
]\loadedtable
\end{codeexample}

    There is one more specialty: you can use |columns=|\marg{column list} to
    reduce the runtime complexity of this command. This works only if the
    |columns| key is provided directly into \meta{options}. In this case
    |\thisrow| and its variants are only defined for those columns listed in
    the |columns| value.


    \paragraph{Limitations.}

    Currently, you can only access three values of one column at a time: the
    current row, the previous row and the next row. Access to arbitrary indices
    is not (yet) supported.


    \paragraph{Remark:}

    If you'd like to create a table from scratch using this command (or the
    related |create on use| simplification), take a look at
    |\pgfplotstablenew|.

    The default implementation of |assign| is to produce empty strings. The
    default implementation of |assign last| is to invoke |assign|, so in case
    you never really use the next row's value, you won't need to touch
    |assign last|. The same holds for |assign first|.
\end{command}

\begin{pgfplotstablecreateonusekey}
    Allows ``lazy creation'' of the column \meta{col name}. Whenever the column
    \meta{col name} is queried by name, for example in an
    |\pgfplotstabletypeset| command, and such a column does not exist already,
    it is created on the fly.
    %
\begin{codeexample}[narrow]
% requires \usepackage{array}
\pgfplotstableset{% could be used in preamble
    create on use/quot1/.style=
        {create col/quotient={error1}}}

\pgfplotstabletypeset[
    columns={error1,quot1},
    columns/error1/.style={sci,sci zerofill},
    columns/quot1/.style={dec sep align}]
{pgfplotstable.example1.dat}
\end{codeexample}
    %
    The example above queries |quot1| which does not yet exist in the input
    file. Therefore, it is checked whether a |create on use| style for |quot1|
    exists. This is the case, so it is used to create the missing column. The
    |create col/quotient| key is discussed below; it computes quotients of
    successive rows in column |error1|.

    A |create on use| specification is translated into

    |\pgfplotstablecreatecol[|\meta{create options}|]|\marg{col name}\marg{the table},

    or, equivalently, into

    |\pgfplotstablecreatecol[|create on use/\meta{col name}|]|\marg{col name}\marg{the table}.

    This feature allows some laziness, because you can omit the lengthy table
    modifications. However, laziness may cost something: in the example above,
    the generated column will be \emph{lost} after returning from
    |\pgfplotstabletypeset|.

    The |create on use| has higher priority than |alias|.

    In case \meta{col name} contains characters which are required for key
    settings, you need to use braces around it:
    ``|create on use/{name=wi/th,special}/.style={...}|''.

    More examples for |create on use| are shown below while discussing the
    available column creation styles.

    Note that |create on use| is also available within \PGFPlots{}, in
    |\addplot table| when used together with the |read completely| key.
\end{pgfplotstablecreateonusekey}


\subsection{Predefined Column Generation Methods}

The following keys can be used in both |\pgfplotstablecreatecol| and the easier
|create on use| frameworks.


\subsubsection{Acquiring Data Somewhere}

\begin{stylekey}{/pgfplots/table/create col/set=\marg{value}}
    A style for use in column creation context which creates a new column and
    writes \meta{value} into each new cell. The value is written as string
    (verbatim).
    %
\begin{codeexample}[]
\pgfplotstableset{
    create on use/my new col/.style={create col/set={--empty--}},
    columns/my new col/.style={string type}
}

\pgfplotstabletypeset[
    columns={level,my new col},
]{pgfplotstable.example1.dat}
\end{codeexample}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/set list=\marg{comma-separated-list}}
    A style for use in column creation context which creates a new column
    consisting of the entries in \meta{comma-separated-list}. The value is
    written as string (verbatim).

    The \meta{comma-separated-list} is processed via \Tikz's |\foreach|
    command, that means you can use |...| expressions to provide number (or
    character) ranges.
    %
\begin{codeexample}[]
\pgfplotstableset{
    create on use/my new col/.style={
        create col/set list={A,B,C,4,50,55,...,100}},
    columns/my new col/.style={string type}
}

\pgfplotstabletypeset[
    columns={level,my new col},
]{pgfplotstable.example1.dat}
\end{codeexample}
    %
    \noindent The new column will be padded or truncated to the required number
    of rows. If the list does not contain enough elements, empty cells will be
    produced.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/copy=\marg{column name}}
    A style for use in column creation context which simply copies the existing
    column \meta{column name}.
    %
\begin{codeexample}[]
\pgfplotstableset{
    create on use/new/.style={create col/copy={level}}
}

\pgfplotstabletypeset[
    columns={level,new},
    columns/new/.style={column name=Copy of level}
]{pgfplotstable.example1.dat}
\end{codeexample}
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/copy column from table=\marg{file name or \textbackslash macro}\marg{column name}}
    A style for use in column creation context which creates a new column
    consisting of the entries in \meta{column name} of the provided table. The
    argument may be either a file name or an already loaded table (i.e.\@ a
    \meta{\textbackslash macro} as returned by |\pgfplotstableread|).

    You can use this style, possibly combined with |\pgfplotstablenew|, to
    merge one common sort of column from different tables into one large table.

    The cell values are written as string (verbatim).

    \noindent The new column will be padded or truncated to the required number
    of rows. If the list does not contain enough elements, empty cells will be
    produced.
\end{stylekey}


\subsubsection{Mathematical Operations}

\begin{key}{/pgf/fpu=\mchoice{true,false} (initially true)}
        \index{Precision}
    Before we start to describe the column generation methods, one word about
    the math library. The core is always the \PGF{} math engine written by Mark
    Wibrow and Till Tantau. However, this engine has been written to produce
    graphics and is not suitable for scientific computing.

    I added a high-precision floating point library to \PGF{} which will be
    part of releases newer than \PGF{} $2.00$. It offers the full range of IEEE
    double precision computing in \TeX. This FPU is also part of
    \PGFPlotstable{}, and it is activated by default for |create col/expr| and
    all other predefined mathematical methods.

    The FPU won't be active for newly defined numerical styles (although it is
    active for the predefined mathematical expression parsing styles like
    |create col/expr|). If you want to add own routines or styles, you will
    need to use
    %
\begin{codeexample}[code only]
\pgfkeys{/pgf/fpu=true}
\end{codeexample}
    %
    \noindent in order to activate the extended precision. The standard math
    parser is limited to fixed point numbers in the range of $\pm 16384.00000$.
\end{key}

\begin{stylekey}{/pgfplots/table/create col/expr=\marg{math expression}}
    A style for use in |\pgfplotstablecreatecol| which uses \meta{math
    expression} to assign contents for the new column.
    %
\begin{codeexample}[]
\pgfplotstableset{
    create on use/new/.style={
        create col/expr={\thisrow{level}*2}}
}

\pgfplotstabletypeset[
    columns={level,new},
    columns/new/.style={column name=$2\cdot $level}
]{pgfplotstable.example1.dat}
\end{codeexample}
    %
    The macros |\thisrow|\marg{col name} and |\nextrow|\marg{col name} can be
    used to use values of the existing table.

    Please see |\pgfplotstablecreatecol| for more information.


    \paragraph{Accumulated columns:}

    The |expr| style initializes |\pgfmathaccuma| to |0| before its first
    column. Whenever it computes a new column value, it redefines
    |\pgfmathaccuma| to be the result. That means you can use |\pgfmathaccuma|
    inside of \meta{math expression} to accumulate columns. See
    |create col/expr accum| for more details.


    \paragraph{About the precision and number range:}
        \index{Precision}
        \index{Floating Point Unit}

    Starting with version 1.2, |expr| uses a floating point unit. The FPU
    provides the full data range of scientific computing with a relative
    precision between $10^{-4}$ and $10^{-6}$. The |/pgf/fpu| key provides some
    more details.


    \paragraph{Accepted operations:}

    The math parser of \PGF, combined with the FPU, provides the following
    function and operators:

    |+|, |-|, |*|, |/|, |abs|, |round|, |floor|, |mod|, |<|, |>|, |max|, |min|,
    |sin|, |cos|, |tan|, |deg| (conversion from radians to degrees), |rad|
    (conversion from degrees to radians), |atan|, |asin|, |acos|, |cot|, |sec|,
    |cosec|, |exp|, |ln|, |sqrt|, the constanst |pi| and |e|, |^| (power
    operation), |factorial|\footnote{Starting with \PGF{} versions newer than
    $2.00$, you can use the postfix operator \texttt{!} instead of
    \texttt{factorial}.}, |rand| (random between $-1$ and $1$ following a
    uniform distribution), |rnd| (random between $0$ and $1$ following a
    uniform distribution), number format conversions |hex|, |Hex|, |oct|, |bin|
    and some more. The math parser has been written by Mark Wibrow and Till
    Tantau~\cite{tikz}, the FPU routines have been developed as part of
    \PGFPlots{}. The documentation for both parts can be found in~\cite{tikz}.
    \textbf{Attention:} Trigonometric functions work with degrees, not with
    radians, unless |trig format| is reconfigured!
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/expr accum=\marg{math expression}\marg{accum initial}}
    A variant of |create col/expr| which also allows to define the initial
    value of |\pgfmathaccuma|. The case \meta{accum initial}=|0| is
    \emph{equivalent} to |expr=|\marg{math expression}.
    %
\begin{codeexample}[]
\pgfplotstableset{
    create on use/new/.style={
        create col/expr={\pgfmathaccuma + \thisrow{level}}},
    create on use/new2/.style={
        create col/expr accum={\pgfmathaccuma * \thisrow{level}}{1}%<- start with `1'
    }
}

\pgfplotstabletypeset[
    columns={level,new,new2},
    columns/new/.style={column name=$\sum$level},
    columns/new2/.style={column name=$\prod$level}
]{pgfplotstable.example1.dat}
\end{codeexample}
    %
    The example creates two columns: the |new| column is just the sum of each
    value in the \meta{level} column (it employs the default
    |\pgfmathaccuma=0|). The |new2| column initializes |\pgfmathaccuma=100| and
    then successively subtracts the value of \meta{level}.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/quotient=\marg{column name}}
    A style for use in |\pgfplotstablecreatecol| which computes the quotient
    $c_i := m_{i-1} / m_i$ for every entry $i = 1,\dotsc, (n-1)$ in the column
    identified with \meta{column name}. The first value $c_0$ is kept empty.
    %
\begin{codeexample}[]
% requires \usepackage{array}
\pgfplotstableset{% configuration, for example, in preamble:
    create on use/quot1/.style={create col/quotient=error1},
    create on use/quot2/.style={create col/quotient=error2},
    columns={error1,error2,quot1,quot2},
    %
    % display styles:
    columns/error1/.style={sci,sci zerofill},
    columns/error2/.style={sci,sci zerofill},
    columns/quot1/.style={dec sep align},
    columns/quot2/.style={dec sep align}
}

\pgfplotstabletypeset{pgfplotstable.example1.dat}
\end{codeexample}
    %
    This style employs methods of the floating point unit, that means it works
    with a relative precision of about $10^{-7}$ ($7$ significant digits in the
    mantissa).
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/iquotient=\marg{column name}}
    Like |create col/quotient|, but the quotient is inverse.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/dyadic refinement rate=\marg{column name}}
    A style for use in |\pgfplotstablecreatecol| which computes the convergence
    rate $\alpha$ of the data in column \meta{column name}. The contents of
    \meta{column name} is assumed to be something like $e_i(h_i) =
    O(h_i^\alpha)$. Assuming a dyadic refinement relation from one row to the
    next, $h_i = h_{i-1}/2$, we have $h_{i-1}^\alpha / (h_{i-1}/2)^\alpha =
    2^\alpha$, so we get $\alpha$ using
    %
        \[
            c_i := \log_2\left( \frac{e_{i-1}}{e_i} \right).
        \]
    %
    The first value $c_0$ is kept empty.
    %
\begin{codeexample}[]
% requires \usepackage{array}
\pgfplotstabletypeset[% here, configuration options apply only to this single statement:
    create on use/rate1/.style={create col/dyadic refinement rate={error1}},
    create on use/rate2/.style={create col/dyadic refinement rate={error2}},
    columns={error1,error2,rate1,rate2},
    columns/error1/.style={sci,sci zerofill},
    columns/error2/.style={sci,sci zerofill},
    columns/rate1/.style={dec sep align},
    columns/rate2/.style={dec sep align}]
    {pgfplotstable.example1.dat}
\end{codeexample}
    %
    This style employs methods of the floating point unit, that means it works
    with a relative precision of about $10^{-6}$ ($6$ significant digits in the
    mantissa).
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/idyadic refinement rate=\marg{column name}}
    As |create col/dyadic refinement rate|, but the quotient is inverse.
\end{stylekey}

\begin{keylist}{%
    /pgfplots/table/create col/gradient=\marg{col x}\marg{col y},
    /pgfplots/table/create col/gradient loglog=\marg{col x}\marg{col y},
    /pgfplots/table/create col/gradient semilogx=\marg{col x}\marg{col y},
    /pgfplots/table/create col/gradient semilogy=\marg{col x}\marg{col y}%
}
    A style for |\pgfplotstablecreatecol| which computes piecewise gradients
    $(y_{i+1} - y_i) / (x_{i+1} - x_i )$ for each row. The $y$ values are taken
    out of column \meta{col y} and the $x$ values are taken from \meta{col y}.

    The logarithmic variants apply the natural logarithm, $\log(\cdot)$, to its
    argument before starting to compute differences. More precisely, the
    |loglog| variant applies the logarithm to both $x$ and $y$, the |semilogx|
    variant applies the logarithm only to~$x$ and the |semilogy| variant
    applies the logarithm only to~$y$.
    %
\begin{codeexample}[]
% requires \usepackage{array}
\pgfplotstableset{% configuration, for example in preamble:
    create on use/slopes1/.style={create col/gradient loglog={dof}{error1}},
    create on use/slopes2/.style={create col/gradient loglog={dof}{error2}},
    columns={dof,error1,error2,slopes1,slopes2},
    % display styles:
    columns/dof/.style={int detect},
    columns/error1/.style={sci,sci zerofill},
    columns/error2/.style={sci,sci zerofill},
    columns/slopes1/.style={dec sep align},
    columns/slopes2/.style={dec sep align}
}
\pgfplotstabletypeset{pgfplotstable.example1.dat}
\end{codeexample}

\begin{codeexample}[]
% requires \usepackage{array}
\pgfplotstableset{% configuration, for example in preamble:
    create on use/slopes1/.style={create col/gradient semilogy={level}{error1}},
    columns={level,error1,slopes1},
    % display styles:
    columns/level/.style={int detect},
    columns/error1/.style={sci,sci zerofill,sci subscript},
    columns/slopes1/.style={dec sep align}
}
\pgfplotstabletypeset{pgfplotstable.example1.dat}
\end{codeexample}
    %
    This style employs methods of the floating point unit, that means it works
    with a relative precision of about $10^{-6}$ ($6$ significant digits in the
    mantissa).
\end{keylist}

\begin{stylekey}{/pgfplots/table/create col/linear regression=\marg{key-value-config}}
    Computes a linear (least squares) regression $y(x) = a \cdot x + b$ using
    the sample data $(x_i,y_i)$ which has to be specified inside of
    \meta{key-value-config}.
    %
\begin{codeexample}[pre={\vbox\bgroup\hsize=3cm},post=\egroup]
% load table from somewhere:
\pgfplotstableread{
    x y
    1 1
    2 4
    3 9
    4 16
    5 25
    6 36
}\loadedtbl

% create the `regression' column:
\pgfplotstablecreatecol[linear regression]
    {regression}
    {\loadedtbl}
% store slope
\xdef\slope{\pgfplotstableregressiona}

\pgfplotstabletypeset\loadedtbl\\

The slope is `\slope'.
\end{codeexample}
    %
    \noindent The example above loads a table from inline data, appends a
    column named `|regression|' and typesets it. Since no
    \meta{key-value-config} has been provided, |x=[index]0| and |y=[index]1|
    will be used. The |\xdef\slope{...}| command stores the `$a$' value of the
    regression line into a newly defined macro `|\slope|'.\footnote{The
    \texttt{\textbackslash xdef} means ``global expanded definition'': it
    expands the argument until it can't be expanded any further and assigns a
    (global) name to the result. See any \TeX{} book for details.}

    The complete documentation for this feature has been moved to \PGFPlots{}
    due to its close relation to plotting. Please refer to the \PGFPlots{}
    manual coming with this package.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/function graph cut y=\marg{cut value}\marg{common options}\marg{one key--value set for each plot}}
    A specialized style for use in |create on use| statements which computes
    cuts of (one or more) discrete plots $y(x_1), \dotsc, y(x_N)$ with a fixed
    \meta{cut value}. The $x_i$ are written into the table's cells.

    In a cost--accuracy plot, this feature allows to extract the cost for fixed
    accuracy. The dual feature with |cut x| allows to compute the accuracy for
    fixed cost.
    %
    \pgfplotsset{anchor=center,/tikz/baseline}
\begin{codeexample}[]
\pgfplotstablenew[
    create on use/cut/.style={create col/function graph cut y=
        {2.5e-4} % search for fixed L2 = 2.5e-4
        {x=Basis,y=L2,ymode=log,xmode=log} % double log, each function is L2(Basis)
        % now, provide each single function f_i(Basis):
        {{table=plotdata/newexperiment1.dat},{table=plotdata/newexperiment2.dat}}
    },
    columns={cut}]
    {2}
    \loadedtable

% Show the data:
\pgfplotstabletypeset{\loadedtable}

\begin{tikzpicture}
\begin{loglogaxis}
    \addplot table[x=Basis,y=L2] {plotdata/newexperiment1.dat};
    \addplot table[x=Basis,y=L2] {plotdata/newexperiment2.dat};
    \draw[blue!30!white] (1,2.5e-4) -- (1e5,2.5e-4);
    \node[pin=-90:{$x=53.66$}] at (53.66,2.5e-4) {};
    \node[pin=45:{$x=601.83$}] at (601.83,2.5e-4) {};
\end{loglogaxis}
\end{tikzpicture}
\end{codeexample}
    %
    In the example above, we are searching for $x_1$ and $x_2$ such that
    $f_1(x_1) = \pgfmathprintnumber{2.5e-4}$ and $f_2(x_2)
    =\pgfmathprintnumber{2.5e-4}$. On the left is the automatically computed
    result. On the right is a problem illustration with proper annotation using
    \PGFPlots{} to visualize the results. The \meta{cut value} is set to
    |2.5e-4|. The \meta{common options} contain the problem setup; in our case
    logarithmic scales and column names. The third argument is a
    comma-separated-list. Each element $i$ is a set of keys describing how to
    get $f_i(\cdot)$.

    During both \meta{common options} and \meta{one key--value set for each
    plot}, the following keys can be used:
    %
    \begin{itemize}
        \item \declareandlabel{table}|=|\marg{table file or \textbackslash
            macro}: either a file name or an already loaded table where to
            get the data points,
        \item \declareandlabel{x}|=|\marg{col name}: the column name of the
            $x$-axis,
        \item \declareandlabel{y}|=|\marg{col name}: the column name of the
            $y$-axis.
        \item \declareandlabel{foreach}|=|\marg{\textbackslash foreach loop
            head}\marg{file name pattern} This somewhat advanced syntax
            allows to collect tables in a loop automatically:
            %
\begin{codeexample}[]
\pgfplotstablenew[
    % same as above...
    create on use/cut/.style={create col/function graph cut y=
        {2.5e-4}% search for fixed L2 = 2.5e-4
        {x=Basis,y=L2,ymode=log,xmode=log,
         foreach={\i in {1,2}}{plotdata/newexperiment\i.dat}}%
        {}% just leave this empty.
    },
    columns={cut}]
    {2}
    \loadedtable
% Show the data:
\pgfplotstabletypeset{\loadedtable}
\end{codeexample}
            %
            \PGFPlotstable{} will call |\foreach |\meta{\textbackslash
            foreach loop head} and it will expand \meta{file name pattern}
            for every iteration. For every iteration, a simpler list entry of
            the form

            |table=|\marg{expanded pattern}|,x=|\marg{value of x}|,y=|\marg{value of y}

            will be generated.

            It is also possible to provide |foreach=| inside of \meta{one
            key--value set for each plot}. The |foreach| key takes precedence
            over |table|. Details about the accepted syntax of |\foreach| can
            be found in the \pgfname\ manual.
    \end{itemize}
    %
    The keys \declareandlabel{xmode} and \declareandlabel{ymode} can take
    either |log| or |linear|. All mentioned keys have the common key path

    \textcolor{red!75!black}{\texttt{/pgfplots/table/create col/function graph cut/}}.
\end{stylekey}

\begin{stylekey}{/pgfplots/table/create col/function graph cut x=\marg{cut value}\marg{common options}\marg{one key--value set for each plot}}
    As above, just with $x$ and $y$ exchanged.
\end{stylekey}


\section{Miscellaneous}

\subsection{Writing (Modified) Tables To Disk}

\begin{key}{/pgfplots/table/outfile=\marg{file name} (initially empty)}
    Writes the completely processed table as \TeX{} file to \meta{file name}.
    This key is described in all detail on page~\pageref{page:outfile}.
\end{key}

\begin{command}{\pgfplotstablesave\oarg{options}\marg{\textbackslash macro or input file name}\marg{output file name}}
    This command takes a table and writes it to a new data file (without
    performing any typesetting).

    If the first argument is a file name, that file is loaded first.

    This command simply invokes |\pgfplotstabletypeset| with cleared output
    parameters. That means any of the column creation methods apply here as
    well, including any postprocessing steps (without the final typesetting).

    |\pgfplotstablesave| uses the keys |reset styles| and
    |disable rowcol styles| to clear any typesetting related options.

    Furthermore, it sets |string type| to allow verbatim output. You may want
    to use |numeric as string type| instead in case you only have numerical
    data -- this will display integers resulting from arithmetics not in
    scientific notation.\footnote{Note however, that \texttt{string type} does
    not round or truncate integers either, even though they are displayed as
    floats.}
    %
\begin{codeexample}[]
\pgfplotstablesave[
    create on use/postproc1/.style={create col/dyadic refinement rate=error1},
    columns={dof,error1,postproc1}
]
    {pgfplotstable.example1.dat}
    {pgfplotstable.example1.out.dat}
\end{codeexample}
    %
    Now, |pgfplotstable.example1.out.dat| is
    %
    \lstinputlisting[basicstyle=\ttfamily\footnotesize,tabsize=8]{pgfplotstable.example1.out.dat}

    You can use the |col sep| key inside of \meta{options} to define a column
    separator for the output file. In case you need a different input column
    separator, use |in col sep| instead of |col sep|.


    \paragraph{Remarks}

    \begin{itemize}
        \item Empty cells will be filled with |{}| if |col sep=space|. Use
            the |empty cells with| style to change that.
        \item Use |disable rowcol styles=false| inside of \meta{options} if
            you need to change column/row based styles.
    \end{itemize}
\end{command}


\subsection{Miscellaneous Keys}

\begin{key}{/pgfplots/table/disable rowcol styles=\mchoice{true,false} (initially false)}
    Set this to |true| if |\pgfplotstabletypeset| shall \emph{not} set any
    styles which apply only to specific columns or only to specific rows.

    This disables the styles
    %
    \begin{itemize}
        \item |columns/|\meta{column name},
        \item |display columns/|\meta{column index},
        \item |every col no |\meta{column index},
        \item |every row no |\meta{row index}.
    \end{itemize}
\end{key}

\begin{key}{/pgfplots/table/reset styles}
    Resets all table typesetting styles which do not explicitly depend on
    column or row names and indices. The affected styles are
    %
    \begin{itemize}
        \item |every table|,
        \item |every even row|, |every odd row|, |every column|,
            |every even column|, |every odd column|,
        \item |every first column|, |every last column|, |every first row|,
            |every last row|,
        \item |every head row|,
        \item |postproc cell content|, |preproc cell content|.
    \end{itemize}
    %
    In case you want to reset all, you should also consider the key
    |disable rowcol styles|.
\end{key}


\subsection{A summary of how to define and use styles and keys}

This section summarizes features of |pgfkeys|. The complete documentation can
be found in the \pgfname{} manual,~\cite{tikz}.

\begin{handler}{{.style}=\marg{key-value-list}}
    Defines or redefines a style \meta{key}. A style is a normal key which will
    set all options in \meta{key-value-list} when it is set.

    Use |\pgfplotstableset{|\meta{key}|/.style={|\meta{key-value-list}|}}| to
    (re)define a style \meta{key} in the namespace |/pgfplots/table|.
\end{handler}

\begin{handler}{{.append style}=\marg{key-value-list}}
    Appends \meta{key-value-list} to an already existing style \meta{key}. This
    is the preferred method to change the predefined styles: if you only
    append, you maintain compatibility with future versions.

    Use |\pgfplotstableset{|\meta{key}|/.append style={|\meta{key-value-list}|}}|
    to append \meta{key-value-list} to the style \meta{key}. This will assume
    the prefix |/pgfplots/table|.
\end{handler}

\begin{handler}{{.initial}=\marg{value}}
    Defines a new \meta{key} and assigns \meta{value}.
\end{handler}

\begin{handler}{{.add}=\marg{before}\marg{after}}
    Changes \meta{key} by prepending \meta{before} and appending \meta{after}.
    %
\begin{codeexample}[]
\pgfplotstableset{columns={a column}}
`\pgfkeysvalueof{/pgfplots/table/columns}';
\pgfplotstableset{columns/.add={}{,another}}
`\pgfkeysvalueof{/pgfplots/table/columns}';
\pgfplotstableset{columns/.add={}{,and one more}}
`\pgfkeysvalueof{/pgfplots/table/columns}'.
\end{codeexample}
    %
    This can be used inside of |\pgfplotsinvokeforeach| or similar (ungrouped!)
    loop constructs.
\end{handler}

\begin{handler}{{.code}=\marg{\TeX{} code}}
    Occasionally, the \PGFPlots{} user interface offers to replace parts of its
    routines. This is accomplished using so called ``code keys''. What it means
    is to replace the original key and its behavior with new \meta{\TeX{}
    code}. Inside of \meta{\TeX{} code}, any command can be used. Furthermore,
    the |#1| pattern will be the argument provided to the key.
    %
\begin{codeexample}[]
\pgfplotsset{
    My Code/.code={This is a pgfkeys feature. Argument=`#1'}}
\pgfplotsset{My Code={is here}}
\end{codeexample}
    %
    The example defines a (new) key named |My Code|. Essentially, it is nothing
    else but a |\newcommand|, plugged into the key--value interface. The second
    statement ``invokes'' the code key.
\end{handler}

\begin{handler}{{.append code}=\marg{\TeX{} code}}
    Appends \meta{\TeX{} code} to an already existing |/.code| key named
    \meta{key}.
\end{handler}

\begin{handler}{{.code 2 args}=\marg{\TeX{} code}}
    As |/.code|, but this handler defines a key which accepts two arguments.
    When the so defined key is used, the two arguments are available as |#1|
    and |#2|.
\end{handler}


\subsection{Plain \TeX{} and Con\TeX{}t support}
\label{sec:pgfplotstable:context}

The table code generator is initialized to produce \LaTeX{} |tabular|
environments. However, it only relies on~`|&|' being the column separator
and~`|\\|' the row terminator. The |column type| feature is more or less
specific to |tabular|, but you can disable it completely. Replace |begin table|
and |end table| with appropriate \TeX{} or Con\TeX{}t commands to change it. If
you have useful default styles (or bug reports), let me know.


\subsection{Basic Level Table Access and Modification}

\PGFPlotstable{} provides several methods to access and manipulate tables at an
elementary level.

Please keep in mind that \PGFPlotstable{} has been written as a tool for table
visualization. As such, it has been optimized for the case of relatively few
rows (although it may have a lot of columns). The runtime for table creation
and modification is currently $O(N^2)$ where $N$ is the number of
rows.\footnote{The runtime for \texttt{plot table} is linear in the number of
rows using a special routine.} This is completely acceptable for tables with
few rows because \TeX{} can process those structures relatively fast. Keep your
tables small! \PGFPlotstable{} is \emph{not} a tool for large-scale matrix
operations.

Tables are always stored as a sequence of column vectors. Therefore, iteration
over all values in one column is simple whereas iteration over all values in
one row is complicated and expensive.

\begin{command}{\pgfplotstableforeachcolumn\meta{table}\textbackslash as\marg{\textbackslash macro}\marg{code}}
    Iterates over every column name of \meta{table}. The \meta{\textbackslash
    macro} will be set to the currently visited column name. Then, \meta{code}
    will be executed. During \meta{code}, |\pgfplotstablecol| denotes the
    current column index (starting with 0).
    %
\begin{codeexample}[]
\begin{minipage}{0.8\linewidth}
\pgfplotstableread{pgfplotstable.example1.dat}\loadedtable
\pgfplotstableforeachcolumn\loadedtable\as\col{%
    column name is `\col'; index is \pgfplotstablecol;\par
}
\end{minipage}
\end{codeexample}

    This routine does not introduce \TeX{} groups, variables inside of
    \meta{code} are not scoped.
\end{command}

\begin{command}{\pgfplotstableforeachcolumnelement\meta{column name}\textbackslash of\meta{table}\textbackslash as\meta{\textbackslash cellcontent}\marg{code}}
    Reports every table cell $t_{ij}$ for a fixed column $j$ in read-only mode.

    For every cell in the column named \meta{column name}, \meta{code} will be
    executed. During this invocation, the macro \meta{\textbackslash
    cellcontent} will contain the cell's content and |\pgfplotstablerow| will
    contain the current row's index.
    %
\begin{codeexample}[]
\begin{minipage}{0.8\linewidth}
\pgfplotstableread{pgfplotstable.example1.dat}\loadedtable
\pgfplotstableforeachcolumnelement{error1}\of\loadedtable\as\cell{%
    I have now cell element `\cell' at row index `\pgfplotstablerow';\par
}
\end{minipage}
\end{codeexample}
    %
    The argument \meta{column name} can also be a column index. In that case,
    it should contain |[index]|\meta{integer}, for example |[index]4|.
    Furthermore, column aliases and columns which should be generated on the
    fly (see |create on use|) can be used for \meta{column name}.

    This routine does not introduce \TeX{} groups, variables inside of
    \meta{code} are not scoped.
\end{command}

\begin{command}{\pgfplotstablemodifyeachcolumnelement\meta{column name}\textbackslash of\meta{table}\textbackslash as\meta{\textbackslash cellcontent}\marg{code}}
    A routine which is similar to |\pgfplotstableforeachcolumnelement|, but any
    changes of \meta{\textbackslash cellcontent} which might occur during
    \meta{code} will be written back into the respective cell.
    %
\begin{codeexample}[]
\pgfplotstableread{pgfplotstable.example1.dat}\loadedtable
\pgfplotstablemodifyeachcolumnelement{error1}\of\loadedtable\as\cell{%
    \edef\cell{\#\pgfplotstablerow: \cell}%
}
\pgfplotstabletypeset[columns=error1,string type]{\loadedtable}
\end{codeexample}

    If \meta{column name} is a column alias or has been created on the fly, a
    new column named \meta{column name} will be created.
\end{command}

\begin{command}{\pgfplotstablegetelem\marg{row}\marg{col}\textbackslash of\meta{table}}
    Selects a single table element at row \meta{row} and column \meta{col}. The
    second argument has the same format as that described in the last
    paragraph: it should be a column name or a column index (in which case it
    needs to be written as |[index]|\meta{number}).

    The return value will be written to |\pgfplotsretval|.
    %
\begin{codeexample}[]
\pgfplotstableread{pgfplotstable.example1.dat}{\loadedtable}
\pgfplotstablegetelem{4}{error1}\of{\loadedtable}
The value (4,error1) is `\pgfplotsretval'.

\pgfplotstablegetelem{2}{[index]0}\of{\loadedtable}
The value (2,0) is `\pgfplotsretval'.
\end{codeexample}

    \paragraph{Attention:}

    If possible, avoid using this command inside of loops. It is quite slow.
\end{command}

\begin{command}{\pgfplotstablegetcolumnnamebyindex\marg{col index}\textbackslash of\meta{table}\textbackslash to\meta{macro}}
    Retrieves the column name at \meta{col index} from a \meta{table} and
    stores it into a \meta{macro}.
    %
\begin{codeexample}[]
\pgfplotstableread{pgfplotstable.example1.dat}{\loadedtable}
\pgfplotstablegetcolumnnamebyindex{4}\of{\loadedtable}\to\pgfplotsretval
The name of column 4 `\pgfplotsretval'.
\end{codeexample}
    %
    \noindent Note that \meta{table} must be a \emph{loaded} table, i.e.\@ it
    must be a macro resulting from |\pgfplotstableread|. Column indices start
    at~$0$.
\end{command}

\begin{commandlist}{%
    \pgfplotstablegetrowsof\marg{file name or \textbackslash loadedtable},
    \pgfplotstablegetcolsof\marg{file name or \textbackslash loadedtable}%
}
    Defines |\pgfplotsretval| to be the number of rows or columns respectively
    in a table.\footnote{It will also assign \texttt{\textbackslash pgfmathresult}
    to the same value.} The argument may be either a file name or an already
    loaded table (the \meta{\textbackslash macro} of |\pgfplotstableread|).
\end{commandlist}

\begin{command}{\pgfplotstablevertcat\marg{\textbackslash table1}\marg{\textbackslash table2 or filename}}
    See page \pageref{table:vertcat} for details about this command.
\end{command}

\begin{command}{\pgfplotstablenew\oarg{options}\marg{row count}\marg{\textbackslash table}}
    See Section~\ref{pgfplotstable:createcol} for details about this command.
\end{command}
\begin{command}{\pgfplotstablecreatecol\oarg{options}\marg{row count}\marg{\textbackslash table}}
    See Section~\ref{pgfplotstable:createcol} for details about this command.
\end{command}

\begin{commandlist}{%
    \pgfplotstabletranspose\oarg{options}\marg{\textbackslash outtable}\marg{\textbackslash table or filename},
    \pgfplotstabletranspose*\oarg{options}\marg{\textbackslash outtable}\marg{\textbackslash table or filename}%
}
    Defines \meta{\textbackslash outtable} to be the transposed of
    \meta{\textbackslash table of filename}. The input argument can be either a
    file name or an already loaded table.

    The version with `|*|' is only interesting in conjunction with the
    |columns| option, see below.
    %
\begin{codeexample}[]
\pgfplotstabletypeset[string type]{pgfplotstable.example3.dat}
\end{codeexample}

\begin{codeexample}[]
\pgfplotstabletranspose\loadedtable{pgfplotstable.example3.dat}
\pgfplotstabletypeset[string type]\loadedtable
\end{codeexample}

    The optional argument \meta{options} can contain options which influence
    the transposition:
    %
    \begin{pgfplotskey}{table/colnames from=\marg{colname} (initially empty)}
        Inside of |\pgfplotstabletranspose|, this key handles how to define
        output column names.

        If \meta{colname} \emph{is} empty (the initial value), the output
        column names will simply be the old row indices, starting with~$0$.

        If \meta{colname} is not empty, it denotes an input column name whose
        cell values will make up the output column names:
        %
\begin{codeexample}[]
\pgfplotstabletranspose[colnames from=c]\loadedtable{pgfplotstable.example3.dat}
\pgfplotstabletypeset[string type]\loadedtable
\end{codeexample}
        %
        The argument \meta{colname} won't appear as cell contents. It is an
        error if the cells in \meta{colname} don't yield unique column names.
    \end{pgfplotskey}

    \begin{pgfplotskey}{table/input colnames to=\marg{name} (initially colnames)}
        Inside of |\pgfplotstabletranspose|, this key handles what to do with
        \emph{input} column names.

        This key will create a further column named \meta{name} which will be
        filled with the input column names (as string type).
        %
\begin{codeexample}[]
\pgfplotstabletranspose[input colnames to=Input]\loadedtable{pgfplotstable.example3.dat}
\pgfplotstabletypeset[string type]\loadedtable
\end{codeexample}
        %
        Set \meta{name} to the empty string to disable this column.
        %
\begin{codeexample}[]
\pgfplotstabletranspose[input colnames to=]\loadedtable{pgfplotstable.example3.dat}
\pgfplotstabletypeset[string type]\loadedtable
\end{codeexample}
    \end{pgfplotskey}

    \begin{pgfplotskey}{table/columns=\marg{list} (initially empty)}
        Inside of |\pgfplotstabletranspose|, this key handles which input
        columns shall be considered for the transposition.

        If \meta{list} is empty, all columns of the input table will be used
        (which is the initial configuration).

        If \meta{list} is not empty, it is expected to be a list of column
        names. Only these columns will be used as input for the transposition,
        just as if the remaining ones weren't there. It is acceptable to
        provide column aliases or |create on use| arguments inside of
        \meta{list}.
        %
\begin{codeexample}[]
\pgfplotstabletranspose[columns={a,b}]\loadedtable{pgfplotstable.example3.dat}
\pgfplotstabletypeset[string type]\loadedtable
\end{codeexample}

        Here is the only difference between |\pgfplotstabletranspose| and
        |\pgfplotstabletranspose*|: the version without `|*|' \emph{resets} the
        |columns| key before it starts whereas the version with `|*|' simply
        uses the actual content of |columns|.
    \end{pgfplotskey}
\end{commandlist}

\begin{command}{\pgfplotstablesort\oarg{options}\meta{\textbackslash resulttable}\meta{\textbackslash table or filename}}
    Sorts \meta{\textbackslash table or filename} according to \meta{options}
    and writes the sorted table to \meta{\textbackslash resulttable}.

    Use the high level |sort| key to enable sorting automatically during
    |\pgfplotstabletypeset|.
    %
\begin{codeexample}[]
\pgfplotstablesort\result{%
    a      b  c
    19     2 [a]
    -6   -14 [b]
     4   -14 [c]
   -11    -9 [d]
    11    14 [e]
    -9    -9 [f]
     1    13 [g]
     8   -10 [h]
    16    18 [i]
    19    -6 [j]
}
\pgfplotstabletypeset[columns/c/.style={string type}]{\result}%
\end{codeexample}

    The sort key and comparison function can be customized using the following
    keys:

    \begin{key}{/pgfplots/table/sort key=\marg{column} (initially [index]0)}
        Specifies the column which contains the sort key. The argument
        \meta{column} can be any of the columns of the input table, including
        |create on use|, |alias| or |[index]|\meta{integer} specifications. The
        initial setting uses the first available column.
    \end{key}

    \begin{key}{/pgfplots/table/sort key from=\marg{table} (initially empty)}
        Allows to load the |sort key| from a different \meta{table}, which can
        be either a \meta{\textbackslash macro} or a \meta{file name}.
    \end{key}

    \begin{key}{/pgfplots/table/sort cmp=\marg{less than routine} (initially float <)}
        Allows to use a different comparison function.

        \begin{pgfplotskeylist}{%
            fixed <,
            fixed >,
            int <,
            int >,
            float <,
            float >,
            date <,
            date >,
            string <,
            string >%
        }
            These styles constitute the predefined comparison functions. The
            |fixed <|, |int <| and |float <| routines operate on numerical data
            where |int <| expects positive or negative integers and the other
            two expect real numbers. The |fixed <| has a considerably smaller
            number range, but is slightly faster than |float <|.

            The |date <| compares dates of the form |YYYY-MM-DD|. The
            |string <| uses lexicographical string comparison based on the
            ASCII character codes of the sort keys. The |string <| routine also
            evaluates ASCII codes of control sequences or active
            characters.\footnote{As long as they haven't been consumed by
            \TeX's preprocessing.}
            %
\begin{codeexample}[]
\pgfplotstablesort[sort cmp=string <]\result{% 'Header' is the column name:
    Header
    the
    quick
    brown
    fox
    jumps
    over
    the
    lazy
    dog
}
\pgfplotstabletypeset[string type]{\result}%
\end{codeexample}
        \end{pgfplotskeylist}

        The argument \meta{less than routine} is actually a style: it is
        supposed to be one or more keys with |/pgfplots/| key prefix.
        Consequently, all these predefined sort comparisons are actually keys
        which define |iflessthan|. For example, we have the definition of
        |string <| as follows:
        %
\begin{codeexample}[code only]
\makeatletter
\pgfplotsset{
    string </.style={%
        iflessthan/.code args={##1##2##3##4}{%
            \t@pgfplots@toka=\expandafter{##1}%
            \t@pgfplots@tokb=\expandafter{##2}%
            \edef\pgfplots@loc@TMPa{{\the\t@pgfplots@toka}{\the\t@pgfplots@tokb}}%
            \expandafter\pgfplotsutilstrcmp\pgfplots@loc@TMPa
            \if1\pgfplotsretval ##3\else ##4\fi
        }%
    },%
}
\end{codeexample}

        \begin{codeargskey}{/pgfplots/iflessthan}{#1#2#3#4}
            Allows to define custom comparison functions (a strict ordering).
            It compares |#1 < #2| and invokes |#3| in case the comparison is
            true and |#4| if not. The comparison will be evaluated in local
            scopes (local variables are freed afterwards).

            In order to be used as value for |sort cmp|, the |iflessthan|
            routine needs to be defined inside of the value
            |sort cmp=|\meta{less than routine}:
            %
\begin{codeexample}[code only]
\pgfplotsset{
    sort cmp={
        iflessthan/.code args={#1#2#3#4}{%
            % here comes your code
        }%
    },
}
\end{codeexample}
        \end{codeargskey}
    \end{key}
\end{command}


\subsection{Repeating Things: Loops}

\begin{command}{\foreach \meta{variables} |in| \meta{list} \marg{commands}}
    A powerful loop command provided by \Tikz, see~\cite[Section
    ``Utilities'']{tikz}.
    %
\begin{codeexample}[]
\foreach \x in {1,2,...,4} {Iterating \x. }%
\end{codeexample}

    A \PGFPlots{} related example could be
    %
\begin{codeexample}[code only]
\foreach \i in {1,2,...,10} {\addplot table {datafile\i}; }%
\end{codeexample}
\end{command}

\noindent The following loop commands come with \PGFPlots{}. They are similar
to the powerful \Tikz{} |\foreach| loop command, which, however, is not always
useful for table processing: the effect of its loop body end after each
iteration.

The following \PGFPlots{} looping macros are an alternative.

\begin{command}{\pgfplotsforeachungrouped \meta{variable} |in| \meta{list} \marg{command}}
    A specialized variant of |\foreach| which can do two things: it does not
    introduce extra groups while executing \meta{command} and it allows to
    invoke the math parser for (simple!)
    \meta{$x_0$}|,|\meta{$x_1$}|,...,|\meta{$x_n$} expressions.
    %
\begin{codeexample}[]
\def\allcollected{}
\pgfplotsforeachungrouped \x in {1,2,...,4} {Iterating \x. \edef\allcollected{\allcollected, \x}}%
All collected = \allcollected.
\end{codeexample}

    A more useful example might be to work with tables:
    %
\begin{codeexample}[code only]
\pgfplotsforeachungrouped \i in {1,2,...,10} {%
    \pgfplotstablevertcat{\output}{datafile\i} % appends `datafile\i' -> `\output'
}%
% since it was ungrouped, \output is still defined (would not work
% with \foreach)
\end{codeexample}

    \paragraph{Remark:}

    The special syntax
    \meta{list}=\meta{$x_0$}|,|\meta{$x_1$}|,...,|\meta{$x_n$},
    i.e.\@ with two leading elements, followed by dots and a final element,
    invokes the math parser for the loop. Thus, it allows larger number ranges
    than any other syntax if |/pgf/fpu| is active. In all other cases,
    |\pgfplotsforeachungrouped| invokes |\foreach| and provides the results
    without \TeX{} groups.
\end{command}

\begin{command}{\pgfplotsinvokeforeach\marg{list} \marg{command}}
    A variant of |\pgfplotsforeachungrouped| (and such also of |\foreach|)
    which replaces any occurrence of |#1| inside of \meta{command} once for
    every element in \meta{list}. Thus, it actually assumes that \meta{command}
    is like a |\newcommand| body.

    In other words, \meta{command} is invoked for every element of \meta{list}.
    The actual element of \meta{list} is available as |#1|.

    As |\pgfplotsforeachungrouped|, this command does \emph{not} introduce
    extra scopes (i.e.\@ it is ungrouped as well).

    The difference to |\foreach \x in |\meta{list}\marg{command} is subtle: the
    |\x| would \emph{not} be expanded whereas |#1| is.
    %
\begin{codeexample}[]
\pgfkeys{
  otherstyle a/.code={[a]},
  otherstyle b/.code={[b]},
  otherstyle c/.code={[c]},
  otherstyle d/.code={[d]}}
\pgfplotsinvokeforeach{a,b,c,d}
    {\pgfkeys{key #1/.style={otherstyle #1}}}
Invoke them: \pgfkeys{key a} \pgfkeys{key b} \pgfkeys{key c} \pgfkeys{key d}
\end{codeexample}
    %
    The counterexample would use a macro (here |\x|) as loop argument:
    %
\begin{codeexample}[]
\pgfkeys{
  otherstyle a/.code={[a]},
  otherstyle b/.code={[b]},
  otherstyle c/.code={[c]},
  otherstyle d/.code={[d]}}
\pgfplotsforeachungrouped \x in {a,b,c,d}
    {\pgfkeys{key \x/.style={otherstyle \x}}}
Invoke them: \pgfkeys{key a} \pgfkeys{key b} \pgfkeys{key c} \pgfkeys{key d}
\end{codeexample}

    \paragraph{Restrictions:}

    You cannot nest this command yet (since it does not introduce protection by
    scopes).
\end{command}


\printindex

\bibliographystyle{abbrv} %gerapali} %gerabbrv} %gerunsrt.bst} %gerabbrv}% gerplain}
\bibliography{pgfplots}
\end{document}
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